JEE Main & Advanced Mathematics Vector Algebra Question Bank

done Modulus of vector Algebra of vectors Total Questions - 119

• question_answer1)
  The perimeter of a triangle with sides \[3\mathbf{i}+4\mathbf{j}+5\mathbf{k},\,\] \[4\mathbf{i}-3\mathbf{j}-5\mathbf{k}\] and \[7\mathbf{i}+\mathbf{j}\] is                                                [MP PET 1991]
  A)
  \[\sqrt{450}\] done clear
  B)
  \[\sqrt{150}\] done clear
  C)
  \[\sqrt{50}\]           done clear
  D)
  \[\sqrt{200}\] done clear
  View Solution play_arrow

• question_answer2)
  If the position vectors of the vertices of a triangle be \[2\mathbf{i}+4\mathbf{j}-\mathbf{k},\] \[4\mathbf{i}+5\mathbf{j}+\mathbf{k}\] and \[3\mathbf{i}+6\mathbf{j}-3\mathbf{k},\] then the triangle is                                                                                                                           [UPSEAT 2004]
  A)
  Right angled           done clear
  B)
  Isosceles done clear
  C)
  Equilateral              done clear
  D)
  Right angled isosceles done clear
  View Solution play_arrow

• question_answer3)
  If one side of a square be represented by the vector \[3\mathbf{i}+4\mathbf{j}+5\mathbf{k},\] then the area of the square is
  A)
  12            done clear
  B)
  13 done clear
  C)
  25            done clear
  D)
  50 done clear
  View Solution play_arrow

• question_answer4)
  If \[\mathbf{a}=2\mathbf{i}+2\mathbf{j}-\mathbf{k}\] and \[|x\,\mathbf{a}|\,\,=1,\] then x =
  A)
  \[\pm \frac{1}{3}\] done clear
  B)
  \[\pm \frac{1}{4}\] done clear
  C)
  \[\pm \frac{1}{5}\] done clear
  D)
  \[\pm \frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer5)
  Which of the following is not a unit vector for all values of q
  A)
  \[(\cos \theta )\mathbf{i}-(\sin \theta )\,\mathbf{j}\]        done clear
  B)
  \[(\sin \theta )\,\mathbf{i}+(\cos \theta )\,\mathbf{j}\] done clear
  C)
  \[(\sin \,\,2\theta )\,\mathbf{i}-(\cos \theta )\,\mathbf{j}\]              done clear
  D)
  \[(\cos \,\,2\theta )\,\mathbf{i}-(\sin \,\,2\theta )\,\mathbf{j}\] done clear
  View Solution play_arrow

• question_answer6)
  If \[\mathbf{a}+\mathbf{b}\] bisects the angle between a and b, then a and b are
  A)
  Mutually perpendicular          done clear
  B)
  Unlike vectors done clear
  C)
  Equal in magnitude done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  If \[\mathbf{a}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}\] and \[\mathbf{b}=3\mathbf{i}+6\mathbf{j}+2\mathbf{k},\] then a vector in the direction of a and having magnitude as |b| is     [IIT 1983]
  A)
  \[7\,(\mathbf{i}+\mathbf{j}+\mathbf{k})\]          done clear
  B)
  \[\frac{7}{3}\,(\mathbf{i}+2\mathbf{j}+2\mathbf{k})\] done clear
  C)
              \[\frac{7}{9}\,(\mathbf{i}+2\mathbf{j}+2\,\mathbf{k})\]    done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer8)
  If \[\mathbf{p}=7\mathbf{i}-2\mathbf{j}+3\mathbf{k}\] and \[\mathbf{q}=3\mathbf{i}+\mathbf{j}+5\mathbf{k},\] then the magnitude of \[\mathbf{p}-2\mathbf{q}\] is                                              [MP PET 1987]
  A)
  \[\sqrt{29}\]           done clear
  B)
  4 done clear
  C)
  \[\sqrt{62}-2\sqrt{35}\]         done clear
  D)
  \[\sqrt{66}\] done clear
  View Solution play_arrow

• question_answer9)
  Let \[\mathbf{a}=\mathbf{i}\] be a vector which makes an angle of \[{{120}^{o}}\]  with a unit vector b. Then the unit vector \[(\mathbf{a}+\mathbf{b})\] is                                                                                                                                             [MP PET 1991]
  A)
  \[-\frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j}\]       done clear
  B)
  \[-\frac{\sqrt{3}}{2}\mathbf{i}+\frac{1}{2}\mathbf{j}\] done clear
  C)
  \[\frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j}\] done clear
  D)
  \[\frac{\sqrt{3}}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}\] done clear
  View Solution play_arrow

• question_answer10)
  If the position vectors of the vertices of a triangle be \[6\mathbf{i}+4\mathbf{j}+5\mathbf{k},\,\,\,4\mathbf{i}+5\mathbf{j}+6\mathbf{k}\] and \[5\mathbf{i}+6\mathbf{j}+4\mathbf{k},\] then the triangle is
  A)
  Right angled          done clear
  B)
  Isosceles done clear
  C)
  Equilateral              done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer11)
  The perimeter of the triangle whose vertices have the position vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\,\,(5\mathbf{i}+3\mathbf{j}-3\mathbf{k})\] and \[(2\mathbf{i}+5\mathbf{j}+9\mathbf{k}),\] is given by                                                                                                              [MP PET 1993]
  A)
  \[15+\sqrt{157}\] done clear
  B)
  \[15-\sqrt{157}\] done clear
  C)
  \[\sqrt{15}-\sqrt{157}\]        done clear
  D)
  \[\sqrt{15}+\sqrt{157}\] done clear
  View Solution play_arrow

• question_answer12)
  The position vectors of two points A and B are \[\mathbf{i}+\mathbf{j}-\mathbf{k}\] and \[2\mathbf{i}-\mathbf{j}+\mathbf{k}\] respectively. Then \[|\overrightarrow{AB}|\,\,=\]                                                                                                                            [BIT Ranchi 1992]
  A)
  2              done clear
  B)
  3 done clear
  C)
  4              done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer13)
  The magnitudes of mutually perpendicular forces a, b and c are 2, 10 and 11 respectively. Then the magnitude of its resultant is                                                                                                     [IIT 1984]
  A)
  12           done clear
  B)
  15 done clear
  C)
  9              done clear
  D)
  None done clear
  View Solution play_arrow

• question_answer14)
  The system of vectors \[\mathbf{i},\,\,\mathbf{j},\,\,\mathbf{k}\] is
  A)
  Orthogonal            done clear
  B)
  Coplanar done clear
  C)
  Collinear done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer15)
  The direction cosines of the resultant of the vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(-\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(\mathbf{i}-\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+\mathbf{j}-\mathbf{k}),\] are
  A)
  \[\left( \frac{1}{\sqrt{2}},\,\,\frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{6}} \right)\] done clear
  B)
  \[\left( \frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}} \right)\] done clear
  C)
  \[\left( -\frac{1}{\sqrt{6}},\,\,-\frac{1}{\sqrt{6}},\,-\,\frac{1}{\sqrt{6}} \right)\]             done clear
  D)
  \[\left( \frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{3}},\,\frac{1}{\sqrt{3}} \right)\] done clear
  View Solution play_arrow

• question_answer16)
  The position vectors of P and Q are \[5\mathbf{i}+4\mathbf{j}+a\mathbf{k}\] and \[-\mathbf{i}+2\mathbf{j}-2\mathbf{k}\] respectively. If the distance between them is 7, then the value of a will be
  A)
  5, 1 done clear
  B)
  5, 1 done clear
  C)
  0, 5         done clear
  D)
  1, 0 done clear
  View Solution play_arrow

• question_answer17)
  A zero vector has
  A)
  Any direction done clear
  B)
  No direction done clear
  C)
  Many directions     done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer18)
  A unit vector a makes an angle \[\frac{\pi }{4}\] with z-axis. If \[\mathbf{a}+\mathbf{i}+\mathbf{j}\] is a unit vector, then a is equal to                                 [IIT 1988]
  A)
  \[\frac{\mathbf{i}}{2}+\frac{\mathbf{j}}{2}+\frac{\mathbf{k}}{\sqrt{2}}\]              done clear
  B)
  \[\frac{\mathbf{i}}{2}+\frac{\mathbf{j}}{2}-\frac{\mathbf{k}}{\sqrt{2}}\] done clear
  C)
  \[-\frac{\mathbf{i}}{2}-\frac{\mathbf{j}}{2}+\frac{\mathbf{k}}{\sqrt{2}}\]               done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer19)
  A force is a
  A)
  Unit vector             done clear
  B)
  Localised vector done clear
  C)
  Zero vector             done clear
  D)
  Free vector done clear
  View Solution play_arrow

• question_answer20)
  If a, b, c, d be the position vectors of the points A, B, C and D respectively referred to same origin O such that no three of these points are collinear and \[\mathbf{a}+\mathbf{c}=\mathbf{b}+\mathbf{d},\] then quadrilateral ABCD is a
  A)
  Square    done clear
  B)
  Rhombus done clear
  C)
  Rectangle               done clear
  D)
  Parallelogram done clear
  View Solution play_arrow

• question_answer21)
  If the position vectors of A and B are \[\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] and \[5\mathbf{i}-2\mathbf{j}+4\mathbf{k},\] then the direction cosine of \[\overrightarrow{AB}\] along y-axis is                                                                                                  [MNR 1989]
  A)
  \[\frac{4}{\sqrt{162}}\]        done clear
  B)
  \[-\frac{5}{\sqrt{162}}\] done clear
  C)
  5              done clear
  D)
  11 done clear
  View Solution play_arrow

• question_answer22)
  If the resultant of two forces is of magnitude P and equal to one of them and perpendicular to it, then the other force is                                                                                                 [MNR 1986]
  A)
  \[P\sqrt{2}\] done clear
  B)
  P done clear
  C)
  \[P\sqrt{3}\]           done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer23)
  The direction cosines of vector \[\mathbf{a}=3\mathbf{i}+4\mathbf{j}+5\mathbf{k}\] in the direction of positive axis of x, is          [MP PET 1991]
  A)
  \[\pm \frac{3}{\sqrt{50}}\]  done clear
  B)
  \[\frac{4}{\sqrt{50}}\] done clear
  C)
  \[\frac{3}{\sqrt{50}}\]          done clear
  D)
  \[-\frac{4}{\sqrt{50}}\] done clear
  View Solution play_arrow

• question_answer24)
  The point having position vectors \[2\mathbf{i}+3\mathbf{j}+4\mathbf{k},\,\,\]\[3\mathbf{i}+4\mathbf{j}+2\mathbf{k},\] \[4\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] are the vertices of                                                                                                                        [EAMCET 1988]
  A)
  Right angled triangle             done clear
  B)
  Isosceles triangle done clear
  C)
  Equilateral triangle                done clear
  D)
  Collinear done clear
  View Solution play_arrow

• question_answer25)
  Let \[\alpha ,\,\,\beta ,\,\,\gamma \] be distinct real numbers. The points with position vectors \[\alpha \mathbf{i}+\beta \mathbf{j}+\gamma \mathbf{k},\,\,\beta \mathbf{i}+\gamma \mathbf{j}+\alpha \mathbf{k},\,\,\gamma \mathbf{i}+\alpha \mathbf{j}+\beta \mathbf{k}\]                                                                                     [IIT Screening 1994]
  A)
  Are collinear          done clear
  B)
  Form an equilateral triangle done clear
  C)
  Form a scalene triangle done clear
  D)
  Form a right angled triangle done clear
  View Solution play_arrow

• question_answer26)
  If \[|\mathbf{a}|\,\,=3,\,\,\,|\mathbf{b}|\,\,=4\] and \[|\mathbf{a}+\mathbf{b}|\,\,=5,\] then \[|\mathbf{a}-\mathbf{b}|\,\,=\]                                           [EAMCET 1994]
  A)
  6              done clear
  B)
  5 done clear
  C)
  4              done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer27)
  If OP = 8 and \[\overrightarrow{OP}\] makes angles \[{{45}^{o}}\] and \[{{60}^{o}}\] with OX-axis and OY-axis respectively, then \[\overrightarrow{OP}=\]
  A)
  \[8\,(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\]     done clear
  B)
  \[4\,(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] done clear
  C)
  \[\frac{1}{4}(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\]     done clear
  D)
  \[\frac{1}{8}(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] done clear
  View Solution play_arrow

• question_answer28)
  If a and b are two non-zero and non-collinear vectors, then a + b and a ? b are                      [MP PET 1997]
  A)
  Linearly dependent vectors done clear
  B)
  Linearly independent vectors done clear
  C)
  Linearly dependent and independent vectors done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  If the vectors \[6\mathbf{i}-2\mathbf{j}+3\mathbf{k},\,\,2\mathbf{i}+3\mathbf{j}-6\mathbf{k}\] and \[3\mathbf{i}+6\mathbf{j}-2\mathbf{k}\] form a triangle, then it is                              [Karnataka CET 1999]
  A)
  Right angled          done clear
  B)
  Obtuse angled done clear
  C)
  Equilteral                done clear
  D)
  Isosceles done clear
  View Solution play_arrow

• question_answer30)
  If the resultant of two forces of magnitudes P and Q acting at a point at an angle of \[{{60}^{o}}\] is \[\sqrt{7}Q,\] then P/Q is                                                                                     [Roorkee 1999]
  A)
  1              done clear
  B)
  \[\frac{3}{2}\] done clear
  C)
  2              done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer31)
  The direction cosines of the vector \[3\mathbf{i}-4\mathbf{j}+5\mathbf{k}\] are                                                       [Karnataka CET 2000]
  A)
  \[\frac{3}{5},\,\frac{-4}{5},\frac{1}{5}\]           done clear
  B)
  \[\frac{3}{5\sqrt{2}},\,\frac{-4}{5\sqrt{2}},\frac{1}{\sqrt{2}}\] done clear
  C)
  \[\frac{3}{\sqrt{2}},\,\frac{-4}{\sqrt{2}},\,\frac{1}{\sqrt{2}}\]       done clear
  D)
  \[\frac{3}{5\sqrt{2}},\,\,\frac{4}{5\sqrt{2}},\,\frac{1}{\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer32)
  The position vectors of A and B are \[2\mathbf{i}-9\mathbf{j}-4\mathbf{k}\] and \[6\mathbf{i}-3\mathbf{j}+8\mathbf{k}\] respectively, then the magnitude of \[\overrightarrow{AB}\] is                                                                                     [MP PET 2000]
  A)
  11           done clear
  B)
  12 done clear
  C)
  13           done clear
  D)
  14 done clear
  View Solution play_arrow

• question_answer33)
  If the position vectors of P and Q are \[(\mathbf{i}+3\mathbf{j}-7\mathbf{k})\] and \[(5\mathbf{i}-2\mathbf{j}+4\mathbf{k}),\] then \[|\overrightarrow{PQ}|\] is                [MP PET 2001, 03]
  A)
  \[\sqrt{158}\]         done clear
  B)
  \[\sqrt{160}\] done clear
  C)
  \[\sqrt{161}\]         done clear
  D)
  \[\sqrt{162}\] done clear
  View Solution play_arrow

• question_answer34)
  If a is non zero vector of modulus a and m is a non-zero scalar, then ma is a unit vector if         [MP PET 2002]
  A)
  \[m=\pm 1\]           done clear
  B)
  \[m=\,\,|\mathbf{a}|\] done clear
  C)
  \[m=\frac{1}{|\mathbf{a}|}\] done clear
  D)
  \[m=\pm \,2\] done clear
  View Solution play_arrow

• question_answer35)
  The position vectors of the points A, B, C are \[(2\mathbf{i}+\mathbf{j}-\mathbf{k}),\] \[(3\mathbf{i}-2\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+4\mathbf{j}-3\mathbf{k})\] respectively. These points                                                                         [Kurukshetra CEE 2002]
  A)
  Form an isosceles triangle done clear
  B)
  Form a right-angled triangle done clear
  C)
  Are collinear done clear
  D)
  Form a scalene triangle done clear
  View Solution play_arrow

• question_answer36)
  The vectors \[\overrightarrow{AB}=3\mathbf{i}+4\mathbf{k},\] and \[\overrightarrow{AC}=5\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] are the sides of a triangle ABC. The length of the median through A is                                                                                                                [AIEEE 2003]
  A)
  \[\sqrt{18}\]           done clear
  B)
  \[\sqrt{72}\] done clear
  C)
  \[\sqrt{33}\]           done clear
  D)
  \[\sqrt{288}\] done clear
  View Solution play_arrow

• question_answer37)
  If the position vectors of the vertices A, B, C of a triangle ABC are \[7\mathbf{j}+10\mathbf{k},\] \[-\mathbf{i}+6\mathbf{j}+6\mathbf{k}\] and \[-4\mathbf{i}+9\mathbf{j}+6\mathbf{k}\] respectively, the triangle is                                                                                                [UPSEAT 2004]
  A)
  Equilateral              done clear
  B)
  Isosceles done clear
  C)
  Scalene   done clear
  D)
  Right angled and isosceles also done clear
  View Solution play_arrow

• question_answer38)
  The figure formed by the four points \[\mathbf{i}+\mathbf{j}-\mathbf{k},\,\,\,2\mathbf{i}+3\mathbf{j},\] \[3\mathbf{i}+5\mathbf{j}-2\mathbf{k}\] and \[\mathbf{k}-\mathbf{j}\] is                                 [MP PET 2004]
  A)
  Rectangle               done clear
  B)
  Parallelogram done clear
  C)
  Trapezium              done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  ABC is an isosceles triangle right angled at A. Forces of magnitude \[2\sqrt{2,}\,5\] and 6 act along \[\overrightarrow{BC},\,\,\overrightarrow{CA}\] and \[\overrightarrow{AB}\] respectively. The magnitude of their resultant force is                                                   [Roorkee 1999]
  A)
  4              done clear
  B)
  5 done clear
  C)
  \[11+2\sqrt{2}\]   done clear
  D)
  30 done clear
  View Solution play_arrow

• question_answer40)
  If ABCDEF is a regular hexagon and \[\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}=\lambda \,\overrightarrow{AD},\] then \[\lambda =\]                                      [RPET 1985]
  A)
  2              done clear
  B)
  3 done clear
  C)
  4              done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer41)
  If P and Q be the middle points of the sides BC and CD of the parallelogram ABCD, then \[\overrightarrow{AP}+\overrightarrow{AQ}=\]
  A)
  \[\overrightarrow{AC}\]        done clear
  B)
  \[\frac{1}{2}\overrightarrow{AC}\] done clear
  C)
  \[\frac{2}{3}\overrightarrow{AC}\]    done clear
  D)
  \[\frac{3}{2}\overrightarrow{AC}\] done clear
  View Solution play_arrow

• question_answer42)
  P is a point on the side BC of the \[\Delta \,ABC\] and Q is a point such that \[\overrightarrow{PQ}\] is the resultant of \[\overrightarrow{AP},\,\overrightarrow{PB},\,\overrightarrow{PC}.\] Then ABQC is a
  A)
  Square    done clear
  B)
  Rectangle done clear
  C)
  Parallelogram done clear
  D)
  Trapezium done clear
  View Solution play_arrow

• question_answer43)
  In the figure, a vector x satisfies the equation \[\mathbf{x}-\mathbf{w}=\mathbf{v}\]. Then x =
  A)
  \[2\mathbf{a}+\mathbf{b}+\mathbf{c}\]         done clear
  B)
  \[\mathbf{a}+2\mathbf{b}+\mathbf{c}\] done clear
  C)
  \[\mathbf{a}+\mathbf{b}+2\mathbf{c}\]         done clear
  D)
  \[\mathbf{a}+\mathbf{b}+\mathbf{c}\] done clear
  View Solution play_arrow

• question_answer44)
  A vector coplanar with the non-collinear vectors a and b is
  A)
  \[\mathbf{a}\times \mathbf{b}\]          done clear
  B)
  \[l\ne 0,\,\,m\ne 0,\,\,n\ne 0\] done clear
  C)
  \[\mathbf{a}\,.\,\mathbf{b}\]                done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer45)
  If ABCD is a parallelogram, \[\overrightarrow{AB}=2\,\mathbf{i}+4\,\mathbf{j}-5\,\mathbf{k}\] and \[\overrightarrow{AD}=\,\mathbf{i}+2\,\mathbf{j}+3\,\mathbf{k},\] then the unit vector in the direction of BD is                                                                                                               [Roorkee 1976]
  A)
  \[\frac{1}{\sqrt{69}}\,(\mathbf{i}+2\mathbf{j}-8\mathbf{k})\]     done clear
  B)
  \[\frac{1}{69}\,(\mathbf{i}+2\mathbf{j}-8\,\mathbf{k})\] done clear
  C)
  \[\frac{1}{\sqrt{69}}\,(-\mathbf{i}-2\mathbf{j}+8\mathbf{k})\] done clear
  D)
  \[\frac{1}{69}\,(-\mathbf{i}-2\mathbf{j}+8\,\mathbf{k})\] done clear
  View Solution play_arrow

• question_answer46)
  If a, b and c be three non-zero vectors, no two of which are collinear. If the vector \[\mathbf{a}+2\mathbf{b}\] is collinear with c and \[\mathbf{b}+3\mathbf{c}\] is collinear with a, then (\[\lambda \] being some non-zero scalar) \[\mathbf{a}+2\mathbf{b}+6\mathbf{c}\] is equal to                              [AIEEE 2004]
  A)
  \[\lambda \mathbf{a}\]         done clear
  B)
  \[\lambda \mathbf{b}\] done clear
  C)
  \[\lambda \mathbf{c}\]          done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer47)
  If \[\mathbf{a}=2\mathbf{i}+5\mathbf{j}\] and \[\mathbf{b}=2\mathbf{i}-\mathbf{j},\] then the unit vector along \[y=0\] will be                                   [RPET 1985, 95]
  A)
  \[\frac{\mathbf{i}-\mathbf{j}}{\sqrt{2}}\]         done clear
  B)
  \[ap+bq+cr=0\] done clear
  C)
  \[{{90}^{o}}\]    done clear
  D)
  \[\frac{\mathbf{i}+\mathbf{j}}{\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer48)
  What should be added in vector \[\mathbf{a}=3\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] to get its resultant a unit vector i              [Roorkee 1977]
  A)
  \[-\,2\mathbf{i}-4\mathbf{j}+2\mathbf{k}\] done clear
  B)
  \[-2\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] done clear
  C)
  \[2\mathbf{i}+4\mathbf{j}-2\mathbf{k}\]         done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer49)
  If \[\mathbf{a}=\mathbf{i}+2\mathbf{j}+3\mathbf{k},\,\,\,\mathbf{b}=-\mathbf{i}+2\mathbf{j}+\mathbf{k}\] and \[\mathbf{c}=3\mathbf{i}+\mathbf{j},\] then the unit vector along its resultant is      [Roorkee 1980]
  A)
  \[3\mathbf{i}+5\mathbf{j}+4\mathbf{k}\]       done clear
  B)
  \[\frac{3\mathbf{i}+5\mathbf{j}+4\mathbf{k}}{50}\] done clear
  C)
  \[\frac{3\mathbf{i}+5\mathbf{j}+4\mathbf{k}}{5\sqrt{2}}\]        done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer50)
  In a regular hexagon ABCDEF, \[\overrightarrow{AE}=\]                                                                              [MNR 1984]
  A)
                  \[2\mathbf{a}-3\mathbf{b}\]               done clear
  B)
                  \[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AF}\,\,-\,\overrightarrow{AB}\] done clear
  C)
  \[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AB}\,\,-\,\,\overrightarrow{AF}\]            done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer51)
  \[3\,\,\overrightarrow{OD}+\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}=\]                                                                                                       [IIT 1988]
  A)
  \[\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{OC}\]           done clear
  B)
  \[\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{BD}\] done clear
  C)
  \[\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer52)
  \[\mathbf{p}=2\mathbf{a}-3\mathbf{b},\,\,\,\mathbf{q}=\mathbf{a}-2\mathbf{b}+\mathbf{c},\,\,\mathbf{r}=-3\mathbf{a}+\mathbf{b}+2\mathbf{c};\] where a, b and c being non-zero, non-coplanar vectors, then the vector \[-2\mathbf{a}+3\mathbf{b}-\mathbf{c}\] is equal to
  A)
  \[\mathbf{p}-4\mathbf{q}\] done clear
  B)
  \[\frac{-7\mathbf{q}+\mathbf{r}}{5}\] done clear
  C)
  \[2\mathbf{p}-3\mathbf{q}+\mathbf{r}\]         done clear
  D)
  \[4\mathbf{p}-2\mathbf{r}\] done clear
  View Solution play_arrow

• question_answer53)
  In a trapezium, the vector \[\overrightarrow{BC}=\lambda \overrightarrow{AD}.\] We will then find that \[\mathbf{p}=\overrightarrow{AC}+\overrightarrow{BD}\] is collinear with \[\overrightarrow{AD},\] If \[\mathbf{p}=\mu \overrightarrow{AD},\] then
  A)
  \[\mu =\lambda +1\] done clear
  B)
  \[\lambda =\mu +1\] done clear
  C)
  \[\lambda +\mu =1\]            done clear
  D)
  \[\mu =2+\lambda \] done clear
  View Solution play_arrow

• question_answer54)
  If \[\mathbf{a}=2\mathbf{i}+\mathbf{j}-8\mathbf{k}\] and \[\mathbf{b}=\mathbf{i}+3\mathbf{j}-4\mathbf{k},\] then the magnitude of \[\mathbf{a}+\mathbf{b}=\]                                              [MP PET 1996]
  A)
  13           done clear
  B)
  \[\frac{13}{3}\] done clear
  C)
  \[\frac{3}{13}\]     done clear
  D)
  \[\frac{4}{13}\] done clear
  View Solution play_arrow

• question_answer55)
  A, B, C, D, E are five coplanar points, then \[\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}+\overrightarrow{AE}+\overrightarrow{BE}+\overrightarrow{CE}\] is equal to              [RPET 1999]
  A)
  \[\overrightarrow{DE}\]        done clear
  B)
  \[3\,\overrightarrow{DE}\] done clear
  C)
  \[2\,\overrightarrow{DE}\]   done clear
  D)
  \[4\,\overrightarrow{ED}\] done clear
  View Solution play_arrow

• question_answer56)
  If \[\mathbf{a}=3\mathbf{i}-2\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=2\mathbf{i}-4\mathbf{j}-3\mathbf{k}\] and \[\mathbf{c}=-\mathbf{i}+2\mathbf{j}+2\mathbf{k},\] then \[\mathbf{a}+\mathbf{b}+\mathbf{c}\] is                        [MP PET 2001]
  A)
  \[3\mathbf{i}-4\mathbf{j}\] done clear
  B)
  \[3\mathbf{i}+4\mathbf{j}\] done clear
  C)
  \[4\mathbf{i}-4\mathbf{j}\] done clear
  D)
  \[4\mathbf{i}+4\mathbf{j}\] done clear
  View Solution play_arrow

• question_answer57)
  Five points given by A, B, C, D, E are in a plane. Three forces \[\overrightarrow{AC},\,\,\overrightarrow{AD}\] and \[\overrightarrow{AE}\] act at A and three forces \[\overrightarrow{CB},\,\,\overrightarrow{DB},\,\,\overrightarrow{EB}\] act at B. Then their resultant is                                                                                                        [AMU 2001]
  A)
  \[2\overrightarrow{AC}\]     done clear
  B)
  \[3\overrightarrow{AB}\] done clear
  C)
  \[3\overrightarrow{DB}\]     done clear
  D)
  \[2\overrightarrow{BC}\] done clear
  View Solution play_arrow

• question_answer58)
  The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12N. The magnitude of the two forces are                                                                                                           [AIEEE 2002]
  A)
  13, 5 done clear
  B)
  12, 6 done clear
  C)
  14, 4       done clear
  D)
  11, 7 done clear
  View Solution play_arrow

• question_answer59)
  The unit vector parallel to the resultant vector of \[2\mathbf{i}+4\mathbf{j}-5\mathbf{k}\] and \[\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] is                                 [MP PET 2003]
  A)
  \[\frac{1}{7}\,(3\mathbf{i}+6\mathbf{j}-2\mathbf{k})\] done clear
  B)
  \[\frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}}\] done clear
  C)
  \[\frac{\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{6}}\]               done clear
  D)
  \[\frac{1}{\sqrt{69}}\,(-\mathbf{i}-\mathbf{j}+8\mathbf{k})\] done clear
  View Solution play_arrow

• question_answer60)
  If a, b, c are the position vectors of the vertices A, B, C of the triangle ABC, then the centroid of \[\Delta \,ABC\] is [MP PET 1987]
  A)
  \[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}\] done clear
  B)
  \[\frac{1}{2}\,\left( \mathbf{a}+\frac{\mathbf{b}+\mathbf{c}}{2} \right)\] done clear
  C)
  \[\mathbf{a}+\frac{\mathbf{b}+\mathbf{c}}{2}\]          done clear
  D)
  \[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{2}\] done clear
  View Solution play_arrow

• question_answer61)
  If in the given figure \[\overrightarrow{OA}=\mathbf{a},\,\,\,\overrightarrow{OB}=\mathbf{b}\] and \[AP\,\,:\,\,PB=m\,\,:\,\,n,\] then \[\overrightarrow{OP}=\]                                    [RPET 1981; MP PET 1988]
  A)
  \[\frac{m\,\mathbf{a}+n\,\mathbf{b}}{m+n}\]                done clear
  B)
  \[\frac{n\,\mathbf{a}+m\,\mathbf{b}}{m+n}\] done clear
  C)
  \[m\,\mathbf{a}-n\,\mathbf{b}\]          done clear
  D)
  \[\frac{m\,\mathbf{a}-n\,\mathbf{b}}{m-n}\] done clear
  View Solution play_arrow

• question_answer62)
  If D, E, F be the middle points of the sides BC, CA and AB of the triangle ABC, then \[\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF}\] is
  A)
  A zero vector          done clear
  B)
  A unit vector done clear
  C)
  0              done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer63)
  If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that \[\overrightarrow{AC}=3\overrightarrow{AB}\] is                                                                                           [MNR 1980; MP PET 1995, 99]
  A)
  \[3\mathbf{a}-\mathbf{b}\] done clear
  B)
  \[3\mathbf{b}-\mathbf{a}\] done clear
  C)
  \[3\mathbf{a}-2\mathbf{b}\]               done clear
  D)
  \[3\mathbf{b}-2\mathbf{a}\] done clear
  View Solution play_arrow

• question_answer64)
  The position vectors of A and B are \[\mathbf{i}-\mathbf{j}+2\mathbf{k}\] and \[3\mathbf{i}-\mathbf{j}+3\mathbf{k}.\] The position vector of the middle point of the line AB is                                                                                                        [MP PET 1988]
  A)
  \[\frac{1}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}+\mathbf{k}\]        done clear
  B)
  \[2\mathbf{i}-\mathbf{j}+\frac{5}{2}\mathbf{k}\] done clear
  C)
  \[\frac{3}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}+\frac{3}{2}\mathbf{k}\]     done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer65)
  If ABCD is a parallelogram and the position vectors of A, B, C are \[\mathbf{i}+3\mathbf{j}+5\mathbf{k},\,\,\mathbf{i}+\mathbf{j}+\mathbf{k}\] and \[7\mathbf{i}+7\mathbf{j}+7\mathbf{k},\] then the position vector of D will be
  A)
  \[7\mathbf{i}+5\mathbf{j}+3\mathbf{k}\]       done clear
  B)
  \[7\mathbf{i}+9\mathbf{j}+11\mathbf{k}\] done clear
  C)
  \[9\mathbf{i}+11\mathbf{j}+13\mathbf{k}\]  done clear
  D)
  \[8\mathbf{i}+8\mathbf{j}+8\mathbf{k}\] done clear
  View Solution play_arrow

• question_answer66)
  P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then \[\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}=\]                    [RPET 1989; J & K 2005]
  A)
  \[\overrightarrow{OP}\]        done clear
  B)
  \[2\,\,\overrightarrow{OP}\] done clear
  C)
  \[3\,\,\overrightarrow{OP}\] done clear
  D)
  \[4\,\,\overrightarrow{OP}\] done clear
  View Solution play_arrow

• question_answer67)
  If the position vectors of the point A, B, C be i, j, k respectively and P be a point such that \[\overrightarrow{AB}=\overrightarrow{CP},\] then the position vector of P is
  A)
  \[-\mathbf{i}+\mathbf{j}+\mathbf{k}\]            done clear
  B)
  \[-\mathbf{i}-\mathbf{j}+\mathbf{k}\] done clear
  C)
  \[\mathbf{i}+\mathbf{j}-\mathbf{k}\]                done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer68)
  If the position vectors of the points A, B, C, D be \[2\mathbf{i}+3\mathbf{j}+5\mathbf{k},\] \[\mathbf{i}+2\mathbf{j}+3\mathbf{k},\,\,-5\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] and \[\mathbf{i}+10\mathbf{j}+10\mathbf{k}\] respectively, then                                                                                        [MNR 1982]
  A)
  \[\overrightarrow{AB}=\overrightarrow{CD}\] done clear
  B)
  \[\overrightarrow{AB}\,\,\,|\,\,|\,\,\,\overrightarrow{\,CD}\] done clear
  C)
  \[\overrightarrow{AB}\,\,\bot \,\,\overrightarrow{CD}\]    done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer69)
  If the position vector of one end of the line segment AB be \[2\mathbf{i}+3\mathbf{j}-\mathbf{k}\] and the position vector of its middle point be \[3\,(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] then the position vector of the other end is
  A)
  \[4\mathbf{i}+3\mathbf{j}+5\mathbf{k}\]       done clear
  B)
  \[4\mathbf{i}-3\mathbf{j}+7\mathbf{k}\] done clear
  C)
  \[4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\] done clear
  D)
  \[4\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] done clear
  View Solution play_arrow

• question_answer70)
  If G and G' be the centroids of the triangles ABC and \[A'B'C'\] respectively, then \[\overrightarrow{AA}'+\overrightarrow{BB'}+\overrightarrow{CC}'=\]
  A)
  \[\frac{2}{3}\overrightarrow{GG}'\]   done clear
  B)
  \[\overrightarrow{GG}'\] done clear
  C)
  \[2\,\overrightarrow{GG}'\]  done clear
  D)
  \[3\,\overrightarrow{GG}'\] done clear
  View Solution play_arrow

• question_answer71)
  If O be the circumcentre and O' be the orthocentre of the triangle ABC, then \[\overrightarrow{O'A}+\overrightarrow{O'B}+\overrightarrow{O'C}=\]
  A)
  \[\overrightarrow{OO}'\]      done clear
  B)
  \[2\,\overrightarrow{O'O}\] done clear
  C)
  \[2\,\overrightarrow{OO'}\]  done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer72)
  If the vectors represented by the sides AB and BC of the regular hexagon ABCDEF be a and b, then the vector represented by \[\overrightarrow{AE}\] will be
  A)
  \[2\,\mathbf{b}-\mathbf{a}\] done clear
  B)
  \[\mathbf{b}-\mathbf{a}\] done clear
  C)
  \[2\,\mathbf{a}-\mathbf{b}\]               done clear
  D)
  \[\mathbf{a}+\mathbf{b}\] done clear
  View Solution play_arrow

• question_answer73)
  The position vector of a point C with respect to B is \[\mathbf{i}+\mathbf{j}\] and that of B with respect to A is \[\mathbf{i}-\mathbf{j}.\] The position vector of C with respect to A is                                                                                      [MP PET 1989]
  A)
  2 i           done clear
  B)
  2 j done clear
  C)
  2 j           done clear
  D)
  2 i done clear
  View Solution play_arrow

• question_answer74)
  A and B are two points. The position vector of A is \[6\mathbf{b}-2\mathbf{a}.\] A point P divides the line AB in the ratio 1 : 2. If \[\mathbf{a}-\mathbf{b}\] is the position vector of P, then the position vector of B is given by                                                         [MP PET 1993]
  A)
  \[7\mathbf{a}-15\mathbf{b}\] done clear
  B)
  \[7\mathbf{a}+15\mathbf{b}\] done clear
  C)
  \[2\pi /3\] done clear
  D)
  \[15\mathbf{a}+7\mathbf{b}\] done clear
  View Solution play_arrow

• question_answer75)
  If the position vectors of the points A and B are \[c=(2\,-2,\,4)\] and \[3\mathbf{i}-\mathbf{j}-3\mathbf{k},\] then what will be the position vector of the mid-point of AB                                                                                              [MP PET 1992]
  A)
  \[\mathbf{i}+2\mathbf{j}-\mathbf{k}\]             done clear
  B)
  \[2\mathbf{i}+\mathbf{j}-2\mathbf{k}\] done clear
  C)
  \[2\mathbf{i}+\mathbf{j}-\mathbf{k}\]             done clear
  D)
  \[\mathbf{i}+\mathbf{j}-2\mathbf{k}\] done clear
  View Solution play_arrow

• question_answer76)
  If C is the middle point of AB and P is any point outside AB, then                 [MNR 1991; UPSEAT 2000; AIEEE 2005]
  A)
  \[\overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC}\]           done clear
  B)
  \[\overrightarrow{PA}+\overrightarrow{PB}=2\,\overrightarrow{PC}\] done clear
  C)
  \[\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0\]     done clear
  D)
  \[\overrightarrow{PA}+\overrightarrow{PB}+2\,\overrightarrow{PC}=0\] done clear
  View Solution play_arrow

• question_answer77)
  If in a triangle \[\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{b}\] and D, E are the mid-points of AB and AC respectively, then \[\overrightarrow{DE}\] is equal to [RPET 1986]
  A)
  \[\frac{\mathbf{a}}{4}-\frac{\mathbf{b}}{4}\] done clear
  B)
  \[\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{2}\] done clear
  C)
  \[\frac{\mathbf{b}}{4}-\frac{\mathbf{a}}{4}\] done clear
  D)
  \[\frac{\mathbf{b}}{2}-\frac{\mathbf{a}}{2}\] done clear
  View Solution play_arrow

• question_answer78)
  In the triangle ABC, \[\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{c},\,\,\overrightarrow{BC}=\mathbf{b}\], then                                                                                 [RPET 1984]
  A)
  \[\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\]     done clear
  B)
  \[\mathbf{a}+\mathbf{b}-\mathbf{c}=\mathbf{0}\] done clear
  C)
  \[\mathbf{a}-\mathbf{b}+\mathbf{c}=\mathbf{0}\]       done clear
  D)
  \[-\,\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\] done clear
  View Solution play_arrow

• question_answer79)
  ABCDE is a pentagon. Forces \[\overrightarrow{AB},\,\overrightarrow{AE},\,\overrightarrow{DC},\,\overrightarrow{ED}\] act at a point. Which force should be added to this system to make the resultant \[{{\cos }^{-1}}\frac{4}{5}\]                                                                                                            [MNR 1984]
  A)
  \[\overrightarrow{AC}\]        done clear
  B)
  \[\overrightarrow{AD}\] done clear
  C)
  \[\overrightarrow{BC}\]        done clear
  D)
  \[\overrightarrow{BD}\] done clear
  View Solution play_arrow

• question_answer80)
  Let A and B be points with position vectors a and b with respect to the origin O. If the point C on OA is such that \[2AC=CO,\,\,CD\] is parallel to OB and \[|\overrightarrow{CD}|\,\,=\,\,3|\overrightarrow{OB}|,\] then \[\overrightarrow{AD}\] is equal to
  A)
  \[3\mathbf{b}-\frac{\mathbf{a}}{2}\]                done clear
  B)
  \[3\mathbf{b}+\frac{\mathbf{a}}{2}\] done clear
  C)
  \[3\mathbf{b}-\frac{\mathbf{a}}{3}\] done clear
  D)
  \[3\mathbf{b}+\frac{\mathbf{a}}{3}\] done clear
  View Solution play_arrow

• question_answer81)
  In a triangle ABC, if \[2\overrightarrow{AC}=3\overrightarrow{CB},\] then \[2\overrightarrow{OA}+3\overrightarrow{OB}\] equals                                                [IIT 1988; Pb. CET 2003]
  A)
  \[5\overrightarrow{OC}\] done clear
  B)
  \[\frac{1}{3}\,(2\mathbf{i}-2\mathbf{j}+\mathbf{k})\] done clear
  C)
  \[\,\overrightarrow{OC}\]     done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer82)
  If \[\overrightarrow{AO}+\overrightarrow{OB}=\overrightarrow{BO}+\overrightarrow{OC},\] then A, B, C form                                                                              [IIT 1983]
  A)
  Equilateral triangle                done clear
  B)
  Right angled triangle done clear
  C)
  Isosceles triangle done clear
  D)
  Line done clear
  View Solution play_arrow

• question_answer83)
  The sum of the three vectors determined by the medians of a triangle directed from the vertices is                                                                                                                  [MP PET 1997]
  A)
  0 done clear
  B)
  1 done clear
  C)
  1              done clear
  D)
  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer84)
  The position vector of the points which divides internally in the ratio 2 : 3 the join of the points \[2\mathbf{a}-3\mathbf{b}\] and \[3\mathbf{a}-2\mathbf{b},\] is                                                                                          [AI CBSE 1985]
  A)
  \[\frac{12}{5}\mathbf{a}+\frac{13}{5}\mathbf{b}\]      done clear
  B)
  \[\frac{12}{5}\mathbf{a}-\frac{13}{5}\mathbf{b}\] done clear
  C)
  \[\frac{3}{5}\mathbf{a}-\frac{2}{5}\mathbf{b}\]            done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer85)
  If position vector of points A, B, C are respectively i, j, k and \[AB=CX,\] then position vector of point X is [MP PET 1994]
  A)
  \[-\,\mathbf{i}+\mathbf{j}+\mathbf{k}\]          done clear
  B)
  \[\mathbf{i}-\mathbf{j}+\mathbf{k}\] done clear
  C)
  \[\mathbf{i}+\mathbf{j}-\mathbf{k}\]                done clear
  D)
  \[\mathbf{i}+\mathbf{j}+\mathbf{k}\] done clear
  View Solution play_arrow

• question_answer86)
  If a and b are P.V. of two points A and B and C divides AB in ratio 2 : 1, then P.V. of C is         [RPET 1996]
  A)
  \[\frac{\mathbf{a}+2\mathbf{b}}{3}\] done clear
  B)
  \[\frac{2\mathbf{a}+\mathbf{b}}{3}\] done clear
  C)
  \[\frac{\mathbf{a}+2}{3}\] done clear
  D)
  \[\frac{\mathbf{a}+\mathbf{b}}{2}\] done clear
  View Solution play_arrow

• question_answer87)
  If \[A,\,B,\,C\] are the vertices of a triangle whose position vectors are a, b, c and G is the centroid of the \[\Delta ABC,\] then \[\overrightarrow{GA}+\overrightarrow{GB}\,+\overrightarrow{GC}\] is                                                                   [Karnataka CET 2000]
  A)
  0 done clear
  B)
  \[\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}\] done clear
  C)
  \[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}\]          done clear
  D)
  \[\frac{\mathbf{a}+\mathbf{b}-\mathbf{c}}{3}\] done clear
  View Solution play_arrow

• question_answer88)
  If O is origin and C is the mid-point of \[A(2,\,\,-1)\] and \[B(-4,\,3)\]. Then  value of \[\overrightarrow{OC}\] is                      [RPET 2001]
  A)
  i + j        done clear
  B)
  i ? j done clear
  C)
  i + j        done clear
  D)
  i ? j done clear
  View Solution play_arrow

• question_answer89)
  If \[ABCDEF\] is regular hexagon, then \[\overrightarrow{AD}\,+\overrightarrow{EB}+\overrightarrow{FC}=\] [Karnataka CET 2002]
  A)
  0              done clear
  B)
  \[2\overrightarrow{AB}\] done clear
  C)
              \[3\overrightarrow{AB}\]     done clear
  D)
  \[4\overrightarrow{AB}\] done clear
  View Solution play_arrow

• question_answer90)
  If position vectors of a point A is a + 2b and a divides AB in the ratio \[2:3\], then the position vector of B is                                                                                                                         [MP PET 2002]
  A)
  2a ? b     done clear
  B)
  b ? 2a done clear
  C)
  a ? 3b     done clear
  D)
  b done clear
  View Solution play_arrow

• question_answer91)
  If \[D,\,E,\,F\] are respectively the mid points of \[AB,\,AC\]and \[BC\] in \[\Delta ABC\], then \[\overrightarrow{BE}\]\[+\overrightarrow{AF}=\]         [EAMCET 2003]
  A)
  \[\overrightarrow{DC}\]       done clear
  B)
  \[\frac{1}{2}\overrightarrow{BF}\] done clear
  C)
  \[2\overrightarrow{BF}\]      done clear
  D)
  \[\frac{3}{2}\overrightarrow{BF}\] done clear
  View Solution play_arrow

• question_answer92)
  If \[4\mathbf{i}+7\mathbf{j}+8\mathbf{k},\,\,\,2\mathbf{i}+3\mathbf{j}+4\mathbf{k}\,\] and \[2\mathbf{i}+5\mathbf{j}+7\mathbf{k}\] are the position vectors of the vertices A, B and C respectively of triangle ABC. The position vector of the point where the bisector of angle A meets BC is        [Pb. CET 2004]
  A)
  \[\frac{1}{3}\,(6\mathbf{i}+13\mathbf{j}+18\mathbf{k})\]          done clear
  B)
  \[\frac{2}{3}\,(6\mathbf{i}+12\mathbf{j}-8\mathbf{k})\] done clear
  C)
  \[\frac{1}{3}\,(-6\mathbf{i}-8\mathbf{j}-9\mathbf{k})\] done clear
  D)
  \[\frac{2}{3}\,(-6\mathbf{i}-12\mathbf{j}+8\mathbf{k})\] done clear
  View Solution play_arrow

• question_answer93)
  If \[\mathbf{a}=\mathbf{i}-\mathbf{j}\] and \[\mathbf{b}=\mathbf{i}+\mathbf{k}\], then a unit vector coplanar with a  and b and perpendicular to a is
  A)
  i               done clear
  B)
  j done clear
  C)
  k              done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer94)
  If the position vectors of the points A, B, C be \[\mathbf{i}+\mathbf{j},\,\,\,\mathbf{i}-\mathbf{j}\] and \[a\,\,\mathbf{i}+b\,\mathbf{j}+c\,\mathbf{k}\] respectively, then the points A, B, C are collinear if
  A)
  \[a=b=c=1\] done clear
  B)
  \[a=1,\,\,b\] and \[c\] are arbitrary scalars done clear
  C)
  \[a=b=c=0\] done clear
  D)
  \[c=0,\,\,a=1\] and b is arbitrary scalars done clear
  View Solution play_arrow

• question_answer95)
  If the points \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\,\mathbf{b}\] be collinear, then k =
  A)
  0              done clear
  B)
  2 done clear
  C)
  2              done clear
  D)
  Any real number done clear
  View Solution play_arrow

• question_answer96)
  If the position vectors of the points A, B, C be \[\mathbf{a},\ \mathbf{b}\], \[3\mathbf{a}-2\mathbf{b}\] respectively, then the points A, B, C are                                                                                     [MP PET 1989]
  A)
  Collinear done clear
  B)
  Non-collinear done clear
  C)
  Form a right angled triangle done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer97)
  If a, b, c are non-collinear vectors such that for some scalars x, y, z, \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=\mathbf{0},\] then                  [RPET 2002]
  A)
  \[x=0,\,\,y=0,\,\,z=0\] done clear
  B)
  \[x\ne 0,\,\,y\ne 0,\,\,z=0\] done clear
  C)
  \[x=0,\,\,y\ne 0,\,\,z\ne 0\]     done clear
  D)
  \[x\ne 0,\,\,y\ne 0,\,\,z\ne 0\] done clear
  View Solution play_arrow

• question_answer98)
  The vectors \[3\,\mathbf{i}+\mathbf{j}-5\,\mathbf{k}\] and \[a\,\mathbf{i}+b\,\mathbf{j}-15\,\mathbf{k}\]are collinear, if             [RPET 1986; MP PET 1988]
  A)
  \[a=3,\,\,b=1\]       done clear
  B)
  \[a=9,\,\,b=1\] done clear
  C)
  \[a=3,\,\,b=3\]       done clear
  D)
  \[a=9,\,\,b=3\] done clear
  View Solution play_arrow

• question_answer99)
  The points with position vectors \[60\,\mathbf{i}+3\,\mathbf{j}\], \[40\,\mathbf{i}-8\mathbf{j},\], \[a\,\mathbf{i}-52\,\mathbf{j}\] are collinear, if \[a=\]                                                             [RPET 1991; IIT 1983; MP PET 2002]
  A)
  40 done clear
  B)
  40 done clear
  C)
  20           done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer100)
  If O be the origin and the position vector of A be \[4\,\mathbf{i}+5\,\mathbf{j},\] then a unit vector parallel to \[\overrightarrow{OA}\] is
  A)
  \[\frac{4}{\sqrt{41}}\mathbf{i}\]        done clear
  B)
  \[\frac{5}{\sqrt{41}}\mathbf{i}\] done clear
  C)
  \[\frac{1}{\sqrt{41}}(4\,\mathbf{i}+5\,\mathbf{j})\] done clear
  D)
  \[\frac{1}{\sqrt{41}}(4\,\mathbf{i}-5\,\mathbf{j})\] done clear
  View Solution play_arrow

• question_answer101)
  If the position vectors of the points A and B be \[2\,\mathbf{i}+3\,\mathbf{j}-\mathbf{k}\] and \[-2\,\mathbf{i}+3\,\mathbf{j}+4\,\mathbf{k},\] then the line AB is parallel to
  A)
  xy-plane done clear
  B)
  yz-plane done clear
  C)
  zx-plane done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer102)
  The points with position vectors \[10\,\mathbf{i}+3\,\mathbf{j},\,\,12\,\mathbf{i}-5\,\mathbf{j}\] and \[a\,\mathbf{i}+11\,\mathbf{j}\] are collinear, if \[a=\]                                                             [MNR 1992; Kurukshetra CEE 2002]
  A)
  8              done clear
  B)
  4 done clear
  C)
  8 done clear
  D)
  12 done clear
  View Solution play_arrow

• question_answer103)
  Three points whose position vectors are \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\mathbf{b}\] will be collinear, if the value of k is                  [IIT 1984]
  A)
  Zero        done clear
  B)
  Only negative real number done clear
  C)
  Only positive real number done clear
  D)
  Every real number done clear
  View Solution play_arrow

• question_answer104)
  If the position vectors of A, B, C, D are \[2\,\mathbf{i}+\mathbf{j},\] \[\mathbf{i}-3\,\mathbf{j},\] \[3\,\mathbf{i}+2\,\mathbf{j}\] and \[\mathbf{i}+\lambda \mathbf{j}\] respectively and \[\overrightarrow{AB}||\overrightarrow{CD}\] , then \[\lambda \] will be                                                                                                                           [RPET 1988]
  A)
  8              done clear
  B)
  6 done clear
  C)
  8              done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer105)
  If the vectors \[3\,\mathbf{i}+2\,\mathbf{j}-\mathbf{k}\]and \[6\,\mathbf{i}-4x\mathbf{j}+y\mathbf{k}\] are parallel, then the value of x and y will be          [RPET 1985, 86]
  A)
  1, ? 2 done clear
  B)
  1, ? 2 done clear
  C)
  1, 2         done clear
  D)
  1, 2 done clear
  View Solution play_arrow

• question_answer106)
   If \[(x,\,\,y,\,\,z)\ne (0,\,\,0,\,\,0)\] and \[(\mathbf{i}+\mathbf{j}+3\,\mathbf{k})\,x+(3\,\mathbf{i}-3\mathbf{j}+\mathbf{k})\,y\]\[+(-4\mathbf{i}+5\mathbf{j})\,z=\lambda \,(x\mathbf{i}+y\mathbf{j}+z\mathbf{k}),\] then the value of l will be                                                                                                                    [IIT 1982; RPET 1984]
  A)
  2, 0         done clear
  B)
  0, ? 2 done clear
  C)
  1, 0         done clear
  D)
  0, ? 1 done clear
  View Solution play_arrow

• question_answer107)
  The vectors a, b and a + b are
  A)
  Collinear done clear
  B)
  Coplanar done clear
  C)
  Non-coplanar        done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer108)
  If a, b, c are the position vectors of three collinear points, then the existence of x, y, z is such that
  A)
  \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0,\,\,x+y+z\ne 0\] done clear
  B)
  \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}\ne 0,\,\,x+y+z=0\] done clear
  C)
  \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}\ne 0,\,\,x+y+z\ne 0\] done clear
  D)
  \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0,\,\,x+y+z=0\] done clear
  View Solution play_arrow

• question_answer109)
  If \[\mathbf{a}=(2,\,\,5)\] and \[\mathbf{b}=(1,\,\,4),\] then the vector parallel to \[(\mathbf{a}+\mathbf{b})\] is
  A)
  (3, 5)       done clear
  B)
  (1, 1) done clear
  C)
  (1, 3) done clear
  D)
  (8, 5) done clear
  View Solution play_arrow

• question_answer110)
  The vectors a and b are non-collinear. The value of x for which the vectors \[\mathbf{c}=(x-2)\,\mathbf{a}+\mathbf{b}\] and \[\mathbf{d}=(2x+1)\,\mathbf{a}-\mathbf{b}\] are collinear, is   
  A)
  1              done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{1}{3}\]        done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer111)
  sThe vectors \[\mathbf{i}+2\mathbf{j}+3\mathbf{k},\] \[\lambda \mathbf{i}+4\mathbf{j}+7\mathbf{k},\] \[-3\mathbf{i}-2\mathbf{j}-5\mathbf{k}\] are collinear, if l equals               [Kurukshetra CEE 1996]
  A)
  3              done clear
  B)
  4 done clear
  C)
  5              done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer112)
  The position vectors of four points P, Q, R, S are \[2\mathbf{a}+4\mathbf{c},\,\] \[5\mathbf{a}+3\sqrt{3}\,\mathbf{b}+4\mathbf{c},\] \[-2\sqrt{3}\mathbf{b}+\mathbf{c}\] and \[2\mathbf{a}+\mathbf{c}\] respectively,  then                                                                                                            [MP PET 1997]
  A)
  \[\overrightarrow{PQ}\] is parallel to \[\overrightarrow{RS}\] done clear
  B)
  \[\overrightarrow{PQ}\] is not parallel to \[\overrightarrow{RS}\] done clear
  C)
  \[\overrightarrow{PQ}\] is equal to \[\overrightarrow{RS}\] done clear
  D)
  \[\overrightarrow{PQ}\] is parallel and equal to \[\overrightarrow{RS}\] done clear
  View Solution play_arrow

• question_answer113)
  If \[\mathbf{a}=(1,\,\,-1)\] and \[\mathbf{b}=(-\,2,\,m)\] are two collinear vectors, then m=                                                     [MP PET 1998]
  A)
  4              done clear
  B)
  3 done clear
  C)
  2 done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer114)
  If three points A, B, C are collinear, whose position vectors are \[\mathbf{i}-2\mathbf{j}-8\mathbf{k},\,\,5\mathbf{i}-2\mathbf{k}\] and \[11\,\mathbf{i}+\,3\,\mathbf{j}+7\mathbf{k}\] respectively, then the ratio in which B divides AC is                                                                      [RPET 1999]
  A)
  1 : 2        done clear
  B)
  2 : 3 done clear
  C)
  2 : 1        done clear
  D)
  1 : 1 done clear
  View Solution play_arrow

• question_answer115)
  If a and b are two non-collinear vectors and \[x\,\mathbf{a}+y\,\mathbf{b}=0\]                                                                        [RPET 2001]
  A)
                  \[x=0\], but y is not necessarily zero done clear
  B)
                  \[y=0\], but x is not necessarily zero done clear
  C)
              \[x=0\], \[y=0\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer116)
  If three points A, B and C have position vectors \[(1,\,x,\,3),\,\,(3,\,4,\,7)\] and \[ap+bq+cr=1\] respectively and if they are collinear, then \[(x,\,y)=\]                                                                                              [EAMCET 2002]
  A)
  (2, ? 3) done clear
  B)
  (? 2, 3) done clear
  C)
  (2, 3)       done clear
  D)
  (? 2, ? 3) done clear
  View Solution play_arrow

• question_answer117)
  a and b are two non-collinear vectors, then \[x\mathbf{a}+y\mathbf{b}\] (where x and y are scalars) represents a vector which is                                                                                     [MP PET 2003]
  A)
  Parallel to b         done clear
  B)
  Parallel to a done clear
  C)
  Coplanar with a and b         done clear
  D)
  None of these        done clear
  View Solution play_arrow

• question_answer118)
  If a, b, c are three non-coplanar vectors such that \[\mathbf{a}+\mathbf{b}+\mathbf{c}=\alpha \,\mathbf{d}\] and \[\mathbf{b}+\mathbf{c}+\mathbf{d}=\beta \,\mathbf{a},\] then \[\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}\] is equal to
  A)
  0 done clear
  B)
                  \[\alpha \text{ }\mathbf{a}\] done clear
  C)
  \[\beta \text{ }\mathbf{b}\]   done clear
  D)
  \[(\alpha +\beta )\,\mathbf{c}\] done clear
  View Solution play_arrow

• question_answer119)
  The value of k for which the vectors \[\mathbf{a}=\mathbf{i}-\mathbf{j}\] and \[\mathbf{b}=-2\,\mathbf{i}+k\,\mathbf{j}\] are collinear is                                 [Pb. CET 2004]
  A)
  2 done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
              \[\frac{1}{3}\]        done clear
  D)
  3 done clear
  View Solution play_arrow