I Electrical potential, II Torque, III Kinetic Energy, IV Momentum. Which of the quantities listed are vectors?
II and IV
I and II
I and III
II and III
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- I. Electrical potential → Scalar
Electric potential (V) has only magnitude (measured in volts) and no direction. It represents the work done per unit charge to bring a test charge from infinity to a point. (The electric field, which is -∇V, is a vector, but potential itself is scalar.)
- II. Torque → Vector
Torque (τ) has both magnitude (τ = r F sinθ) and direction (given by the right-hand rule; perpendicular to the plane of r and F). It is formally a pseudovector (axial vector) defined as τ = r × F.
- III. Kinetic Energy → Scalar
Kinetic energy (½mv²) has only magnitude (in joules) and no direction. It depends only on speed (scalar), not velocity.
- IV. Momentum → Vector
Momentum (p = mv) has both magnitude (mv) and direction (same as velocity). It is a true vector quantity.
Therefore, the vector quantities from the list are II and IV.
