JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank

done Line and Plane Total Questions - 37

• question_answer1)
  The point at which the line joining the points (2, ?3, 1) and (3, ?4, ?5) intersects the plane \[2x+y+z=7\]is [DSSE 1987; MP PET 1991]
  A)
             (1, 2, 7) done clear
  B)
             (1, ?2, 7) done clear
  C)
             (?1, 2, 7) done clear
  D)
             (1, ?2, ?7) done clear
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• question_answer2)
  The point of intersection of the line \[\frac{x}{1}=\frac{y-1}{2}=\frac{z+2}{3}\] and the  plane \[2x+3y+z=0\]is  [MP PET 1989]
  A)
             (0, 1, ?2) done clear
  B)
             (1, 2, 3) done clear
  C)
             (?1, 9, ?25) done clear
  D)
             \[\left( \frac{-1}{11},\frac{9}{11}\frac{-25}{11} \right)\] done clear
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• question_answer3)
  The line \[\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{0}\]is parallel to
  A)
             xy-plane done clear
  B)
             yz-plane done clear
  C)
             zx-plane done clear
  D)
             None of these done clear
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• question_answer4)
  The equation of the plane passing through the origin and perpendicular to the line \[x=2y=3z\]is
  A)
             \[6x+3y+2z=0\] done clear
  B)
             \[x+2y+3z=0\] done clear
  C)
             \[3x+2y+z=0\] done clear
  D)
             None of these done clear
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• question_answer5)
  If the equation of a line and a plane be \[\frac{x+3}{2}=\frac{y-4}{3}=\frac{z+5}{2}\]and\[4x-2y-z=1\]respectively, then
  A)
             Line is parallel to the plane       done clear
  B)
             Line is perpendicular to the plane done clear
  C)
             Line lies in the plane done clear
  D)
             None of these done clear
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• question_answer6)
  The equation of the straight line passing through (1, 2, 3) and perpendicular to the plane \[x+2y-5z+9=0\] is                     [MP PET 1991]
  A)
             \[\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{-5}\] done clear
  B)
             \[\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+5}{3}\] done clear
  C)
             \[\frac{x+1}{1}=\frac{y+2}{2}=\frac{z+3}{-5}\] done clear
  D)
             \[\frac{x+1}{1}=\frac{y+2}{2}=\frac{z-5}{3}\] done clear
  View Solution play_arrow

• question_answer7)
  The equation of the plane passing through the lines \[\frac{x-4}{1}=\frac{y-3}{1}=\frac{z-2}{2}\]and \[\frac{x-3}{1}=\frac{y-2}{-4}=\frac{z}{5}\] is
  A)
             \[11x-y-3z=35\] done clear
  B)
             \[11x+y-3z=35\] done clear
  C)
             \[11x-y+3z=35\] done clear
  D)
             None of these done clear
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• question_answer8)
  The equation of the plane passing through the points         (3,2,2) and (1,0,?1) and parallel to the line \[\frac{x-1}{2}=\frac{y-1}{-2}=\frac{z-2}{3}\], is
  A)
             \[4x-y-2z+6=0\] done clear
  B)
             \[4x-y+2z+6=0\] done clear
  C)
             \[4x-y-2z-6=0\] done clear
  D)
             None of these done clear
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• question_answer9)
  The equation of the plane which bisects the line joining the points (?1, 2, 3) and (3, ?5, 6) at right angle, is
  A)
             \[4x-7y-3z=8\] done clear
  B)
             \[4x+2y-3z=28\] done clear
  C)
             \[4x-7y+3z=28\] done clear
  D)
             \[4x-7y-3z=28\] done clear
  View Solution play_arrow

• question_answer10)
   The line\[\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\]is parallel to the plane  [BIT Ranchi 1991; Pb. CET 1991]
  A)
             \[3x+4y+5z=7\] done clear
  B)
             \[2x+y-2z=0\] done clear
  C)
             \[x+y-z=2\] done clear
  D)
             \[2x+3y+4z=0\] done clear
  View Solution play_arrow

• question_answer11)
  The point where the line \[\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+3}{4}\] meets the plane \[2x+4y-z=1\], is [DSSE 1981]
  A)
             (3, ?1, 1) done clear
  B)
             (3, 1, 1) done clear
  C)
             (1, 1, 3) done clear
  D)
             (1, 3, 1) done clear
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• question_answer12)
   The distance of the  point (?1, ?5, ?10) from the point of intersection of the line \[\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\] and the plane \[x-y+z=5\], is [AISSE 1985; DSSE 1984; MP PET 2002]
  A)
             10 done clear
  B)
             11 done clear
  C)
             12 done clear
  D)
             13 done clear
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• question_answer13)
  The equation of the line passing through (1, 2, 3) and parallel to the planes \[x-y+2z=5\] and \[3x+y+z=6\], is             [DSSE 1986]
  A)
             \[\frac{x-1}{-3}=\frac{y-2}{5}=\frac{z-3}{4}\] done clear
  B)
             \[\frac{x-1}{-3}=\frac{y-2}{-5}=\frac{z-1}{4}\] done clear
  C)
             \[\frac{x-1}{-3}=\frac{y-2}{-5}=\frac{z-1}{-4}\] done clear
  D)
             None of these done clear
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• question_answer14)
  The line drawn from (4, ?1, 2) to the point (?3, 2, 3) meets a plane at right angles at the point (?10, 5, 4), then the equation of plane is [DSSE 1985]
  A)
             \[7x-3y-z+89=0\] done clear
  B)
             \[7x+3y+z+89=0\] done clear
  C)
             \[7x-3y+z+89=0\] done clear
  D)
             None of these done clear
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• question_answer15)
  The ratio in which the line joining the points  (a, b, c) and   (?a, ?c, ?b) is divided by the xy-plane is [MP PET 1994]
  A)
             \[a:b\] done clear
  B)
             \[b:c\] done clear
  C)
             \[c:a\] done clear
  D)
             \[c:b\] done clear
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• question_answer16)
  The line \[\frac{x+3}{3}=\frac{y-2}{-2}=\frac{z+1}{1}\] and the plane \[4x+5y+3z-5=0\] intersect at a point
  A)
             (3, 1, ?2) done clear
  B)
             (3, ? 2, 1) done clear
  C)
             (2, ?1, 3) done clear
  D)
             (?1, ?2, ?3) done clear
  View Solution play_arrow

• question_answer17)
  If line \[\frac{x-{{x}_{1}}}{l}=\frac{y-{{y}_{1}}}{m}=\frac{z-{{z}_{1}}}{n}\] is parallel to the plane \[ax+by+cz+d=0\], then [MNR 1995: MP PET 1995]
  A)
             \[\frac{a}{l}=\frac{b}{m}=\frac{c}{n}\] done clear
  B)
             \[al+bm+cn=0\] done clear
  C)
             \[\frac{a}{l}+\frac{b}{m}+\frac{c}{n}=0\] done clear
  D)
             None of these done clear
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• question_answer18)
  The equation of plane through the line of intersection of planes \[ax+by+cz+d=0\], \[a'x+b'y+c'z+d'=0\] and parallel to the line \[y=0,z=0\] is [Kurukshetra CEE 1998]
  A)
             \[(ab'-a'b)x+(bc'-b'c)y+(ad'-a'd)=0\] done clear
  B)
             \[(ab'-a'b)x+(bc'-b'c)y+(ad'-a'd)z=0\] done clear
  C)
             \[(ab'-a'b)y+(ac'-a'c)z+(ad'-a'd)=0\] done clear
  D)
             None of these done clear
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• question_answer19)
  The equation of the plane which bisects the line joining      (2, 3, 4) and (6, 7, 8) is [CET 1991, 93]
  A)
             \[x+y+z-15=0\] done clear
  B)
             \[x-y+z-15=0\] done clear
  C)
             \[x-y-z-15=0\] done clear
  D)
             \[x+y+z+15=0\] done clear
  View Solution play_arrow

• question_answer20)
  The line \[\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\] is parallel to the plane
  A)
             \[2x+3y+4z=29\] done clear
  B)
             \[3x+4y-5z=10\] done clear
  C)
             \[3x+4y+5z=38\] done clear
  D)
             \[x+y+z=0\] done clear
  View Solution play_arrow

• question_answer21)
  The distance between the line \[\frac{x-1}{3}=\frac{y+2}{-2}=\frac{z-1}{2}\] and the plane \[2x+2y-z=6\] is
  A)
             9 done clear
  B)
             1 done clear
  C)
             2 done clear
  D)
             3 done clear
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• question_answer22)
  The equation of the plane through the origin containing the line \[\frac{x-1}{5}=\frac{y-2}{4}=\frac{z-3}{5}\] is
  A)
             \[2x+5y-6z=0\] done clear
  B)
             \[x+5y-5z=0\] done clear
  C)
             \[x-5y+3z=0\] done clear
  D)
             \[x+y-z=0\] done clear
  View Solution play_arrow

• question_answer23)
  The angle between the line \[\frac{x-2}{a}=\frac{y-2}{b}=\frac{z-2}{c}\] and the plane \[ax+by+cz+6=0\] is
  A)
             \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}} \right)\] done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{60}^{o}}\] done clear
  D)
             \[{{90}^{o}}\] done clear
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• question_answer24)
  The co-ordinates of the point where the line through \[P(3,\,4,\,1)\]  and \[Q(5,1,6)\] crosses the xy-plane are [MP PET 1997]
  A)
             \[\frac{3}{5},\frac{13}{5},\frac{23}{5}\] done clear
  B)
             \[\frac{13}{5},\frac{23}{5},\frac{3}{5}\] done clear
  C)
             \[\frac{13}{5},\frac{23}{5},0\] done clear
  D)
             \[\frac{13}{5},0,\,0\] done clear
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• question_answer25)
  The co-ordinates of the point where the line \[\frac{x-6}{-1}=\frac{y+1}{0}=\frac{z+3}{4}\] meets the plane \[x+y-z=3\]are [MP PET 1998; Pb. CET 2002]
  A)
             (2, 1, 0) done clear
  B)
             (7, ?1, ?7) done clear
  C)
             (1, 2, ?6) done clear
  D)
             (5, ?1, 1) done clear
  View Solution play_arrow

• question_answer26)
  If a plane passes through the point (1,1,1) and is perpendicular to the line \[\frac{x-1}{3}=\frac{y-1}{0}=\frac{z-1}{4}\], then its perpendicular distance from the origin is [MP PET 1998]
  A)
             \[\frac{3}{4}\] done clear
  B)
             \[\frac{4}{3}\] done clear
  C)
             \[\frac{7}{5}\] done clear
  D)
             1 done clear
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• question_answer27)
  The angle between the line \[\frac{x-1}{2}=\] \[\frac{y-2}{1}=\frac{z+3}{-2}\] and the plane \[x+y+4=0\], is [MP PET 1999]
  A)
             \[0{}^\circ \] done clear
  B)
             \[30{}^\circ \] done clear
  C)
             \[45{}^\circ \] done clear
  D)
             \[90{}^\circ \] done clear
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• question_answer28)
  The equation of the plane containing the line \[\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\] and the point (0, 7, ?7) is [Roorkee 1999]
  A)
             \[x+y+z=1\] done clear
  B)
             \[x+y+z=2\] done clear
  C)
             \[x+y+z=0\] done clear
  D)
             None of these done clear
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• question_answer29)
  The xy-plane divides the line joining the points (?1, 3, 4) and (2, ?5, 6) [RPET 2000]
  A)
             Internally in the ratio 2 : 3         done clear
  B)
             Internally in the ratio 3 : 2 done clear
  C)
             Externally in the ratio 2 : 3        done clear
  D)
             Externally in the ratio 3 : 2 done clear
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• question_answer30)
  Under what condition does a straight line \[\frac{x-{{x}_{0}}}{l}=\]\[\frac{y-{{y}_{0}}}{m}=\frac{z-{{z}_{0}}}{n}\] is parallel to the xy-plane [AMU 2000]
  A)
             \[l=0\] done clear
  B)
             \[m=0\] done clear
  C)
             \[n=0\] done clear
  D)
             \[l=0,m=0\] done clear
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• question_answer31)
  The equation of the plane passing through the line \[\frac{x-1}{5}=\frac{y+2}{6}=\frac{z-3}{4}\]and the point (4, 3, 7) is  [MP PET 2001]
  A)
             \[4x+8y+7z=41\] done clear
  B)
             \[4x-8y+7z=41\] done clear
  C)
             \[4x-8y-7z=41\] done clear
  D)
             \[4x-8y+7z=39\] done clear
  View Solution play_arrow

• question_answer32)
  A plane which passes through the point (3, 2, 0) and the line \[\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}\]is [AIEEE 2002]
  A)
             \[x-y+z=1\] done clear
  B)
             \[x+y+z=5\] done clear
  C)
             \[x+2y-z=0\] done clear
  D)
             \[2x-y+z=5\] done clear
  View Solution play_arrow

• question_answer33)
  The ratio in which the line joining the points (2, 4, 5) and  (3, 5, ?4) is divided by the yz-plane is [MP PET 2002; RPET 2002]
  A)
             \[2:3\] done clear
  B)
             \[3:2\] done clear
  C)
             \[-2:3\] done clear
  D)
             \[4:-3\] done clear
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• question_answer34)
  The angle between the line \[\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\] and the plane \[3x+2y-3z=4\]is [MP PET 2003]
  A)
             \[45{}^\circ \] done clear
  B)
             \[0{}^\circ \] done clear
  C)
             \[{{\cos }^{-1}}\left( \frac{24}{\sqrt{29}\sqrt{22}} \right)\] done clear
  D)
             \[90{}^\circ \] done clear
  View Solution play_arrow

• question_answer35)
  The line joining the points (3, 5, ?7) and (?2, 1, 8) meets the yz-plane at point [RPET 2003]
  A)
             \[\left( 0,\,\frac{13}{5},\,2 \right)\] done clear
  B)
             \[\left( 2,\,0,\,\frac{13}{5} \right)\] done clear
  C)
             \[\left( 0,\,2,\,\frac{13}{5} \right)\] done clear
  D)
             (2, 2, 0) done clear
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• question_answer36)
  The point of intersection of the line \[\frac{x-1}{3}=\frac{y+2}{4}=\frac{z-3}{-2}\] and plane \[2x-y+3z-1=0\] is [Orissa JEE 2005]
  A)
             \[(10,\,\,-10,\,3)\] done clear
  B)
             \[(10,\,\,10,\,-3)\] done clear
  C)
             \[(-10,\,\,10,\,3)\] done clear
  D)
             None of these done clear
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• question_answer37)
  The equation of the plane through the point \[(2,-1,-3)\]and parallel to the lines \[\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}\] and \[\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}\] is [Kerala (Engg.) 2005]
  A)
   \[8x+14y+13z+37=0\] done clear
  B)
             \[8x-14y+13z+37=0\] done clear
  C)
             \[8x+14y-13z+37=0\] done clear
  D)
             \[8x+14y+13z-37=0\] done clear
  E)
  (e)       \[8x-14y-13z-37=0\] done clear
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