Free Vector Product MCQs with Answers

1. The vector product of two parallel vectors is

• A. zero
• B. maximum and equal to AB
• C. equal to AB cos theta
• D. a scalar

Explanation: The cross product has magnitude AB sin theta, and sin 0 is zero, so parallel vectors give a null vector. It is maximum for perpendicular vectors, which is the opposite of the dot product and the easiest way to keep the two straight. The result of a cross product is always a vector, never a scalar.

2. The direction of the vector product A cross B is given by

• A. the direction of A
• B. the direction of B
• C. the bisector of the angle between A and B
• D. the right hand rule, perpendicular to the plane containing A and B

Explanation: Curling the fingers of the right hand from A to B points the thumb along A cross B, which is perpendicular to both vectors. Because the sense reverses when the order is swapped, B cross A equals minus A cross B, so the cross product is not commutative. Torque and magnetic force are both defined this way.

3. Torque is defined as

• A. force divided by distance
• B. the scalar product of force and distance
• C. the product of force and the perpendicular distance from the axis to the line of action
• D. force multiplied by time

Explanation: Only the perpendicular distance, the moment arm, counts, which is why pushing a door near its hinge is so ineffective. Written as a vector product, torque is r cross F, with magnitude rF sin theta, so a force directed straight at the axis produces no turning effect at all. Its unit is the newton metre, which is not called a joule even though the dimensions match.