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question_answer1) If a vector \[\overrightarrow{P}\] making angles a, b, and g respectively with the X, Y and Z axes respectively. Then \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma =\]
question_answer2) If the resultant of n forces of different magnitudes acting at a point is zero, then the minimum value of n is [SCRA 2000]
question_answer3) Can the resultant of 2 vectors be zero [IIIT 2000]
question_answer4) The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the, magnitudes of forces [Roorkee 1992; AIEEE 2002]
question_answer5) A vector \[\overrightarrow{a}\] is turned without a change in its length through a small angle \[d\theta .\]The value of \[|\Delta \overrightarrow{a}|\] and \[\Delta a\] are respectively
question_answer6) Find the resultant of three vectors \[\overrightarrow{OA},\,\overrightarrow{OB}\] and \[\overrightarrow{OC}\] shown in the following figure. Radius of the circle is R.
question_answer7) Figure shows ABCDEF as a regular hexagon. What is the value of \[\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}\]
question_answer8) The length of second's hand in watch is 1 cm. The change in velocity of its tip in 15 seconds is [MP PMT 1987]
question_answer9) A particle moves towards east with velocity 5 m/s. After 10 seconds its direction changes towards north with same velocity. The average acceleration of the particle is [CPMT 1997; IIT-JEE 1982]
question_answer10) A force \[\overrightarrow{F}=-K(y\hat{i}+x\hat{j})\] (where K is a positive constant) acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x- axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the forces \[\overrightarrow{F}\] on the particle is [IIT-JEE 1998]
question_answer11) The vectors from origin to the points A and B are \[\overrightarrow{A}=3\hat{i}-6\hat{j}+2\hat{k}\] and \[\overrightarrow{B}=2\hat{i}+\hat{j}-2\hat{k}\] respectively. The area of the triangle OAB be
question_answer12) A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong
question_answer13) The speed of a boat is 5 km/h in still water. It crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water is [IIT 1988; CBSE PMT 1998, 2000]
question_answer14) A man crosses a 320 m wide river perpendicular to the current in 4 minutes. If in still water he can swim with a speed 5/3 times that of the current, then the speed of the current, in m/min is [Roorkee 1998]
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