Question

Which of the following is not the vector quantity?
(A) Torque
(B) Displacement
(C) Velocity
(D) None of the above

Answer 1

Vector quantities involve direction along with magnitude. The quantities having only magnitude and no directions are called scalar quantities. Look over the definition of the mentioned physical quantities and if any of them doesn’t involve direction, it is not a vector quantity.

Complete step by step answer:
Torque:
Torque is the measure of force that can produce a turning effect on an object and cause it to rotate
about its axis. Torque produces angular acceleration in a body; it is equal to the product of the
magnitude of force and the perpendicular distance of line of action of force from the axis of rotation.
$\tau = F \cdot r\sin \theta$
Where $F =$ magnitude of force, $r =$ perpendicular distance and $\theta =$ angle between the
force and perpendicular distance
In vector form, $\tau = \vec r \times \vec F$
Torque involves both direction and magnitude so it is a vector quantity.

Displacement:
It is the shortest distance between the initial position of an object and its final position. Unlike
distance, displacement involves direction along with magnitude so it is a vector quantity.

Velocity:
The rate of change of displacement is called velocity. It has both direction and magnitude so velocity
is a vector quantity.

Additional information:
Even if a quantity has both direction and magnitude, it must obey certain rules to qualify as a vector.
Some of the rules are vector addition, subtraction, multiplication by a scalar, scalar multiplication,
vector multiplication, and differentiation.

Note:
The direction of torque depends on the direction of the force on the axis.
The direction of displacement is an arrow that points from the final position to the final position.
The direction of velocity is directed in the same direction that the object moves.