Among the following physical quantities, which one is not a vector quantity and has only magnitude but no direction?

Introduction / Context:
In mechanics, physical quantities are classified as scalars or vectors. Scalar quantities have only magnitude, while vector quantities possess both magnitude and direction. Many exam questions test whether you can correctly classify common quantities such as speed, velocity, torque, and displacement. This question checks your ability to distinguish between a scalar and similar-looking vector quantities.

Given Data / Assumptions:

• We are given four options: speed, velocity, torque, and displacement.
• We use standard physics definitions of scalar and vector quantities.
• The question asks specifically which quantity is not a vector.
• We assume motion in classical mechanics, not in any relativistic or quantum context.

Concept / Approach:
A vector quantity has both magnitude and a specific direction, and it follows the rules of vector addition. A scalar quantity has magnitude only and does not depend on direction. Velocity is defined as the rate of change of displacement with direction. Displacement and torque are also vector quantities, where displacement describes directed distance and torque represents the turning effect with a specified sense of rotation. Speed, however, is defined as the magnitude of velocity and does not involve direction. Therefore, speed is a scalar, not a vector.

Step-by-Step Solution:
Step 1: Recall that speed is the distance travelled per unit time, without specifying direction. Step 2: Recall that velocity is the displacement per unit time, and it is associated with a definite direction. Step 3: Displacement is the shortest directed distance between initial and final positions, clearly a vector. Step 4: Torque is the cross product of position vector and force, which gives it direction (often represented by the right hand rule). Step 5: Since only speed lacks direction and is described solely by magnitude, it must be a scalar. Step 6: Therefore, the physical quantity that is not a vector is speed.

Verification / Alternative check:
In vector notation, velocity, displacement and torque are usually written with arrow signs or boldface letters, for example v, s, and τ. These quantities add using vector laws such as the triangle or parallelogram rule. Speed is usually written without an arrow, and when you combine speeds you typically do so by normal arithmetic, not by vector addition, unless first converting them to velocities with directions. Textbook tables of scalar and vector quantities consistently list speed as scalar and the other three as vectors, confirming this classification.

Why Other Options Are Wrong:
Velocity: It clearly has direction and magnitude, for example 20 km/h due east, making it a vector quantity.
Torque: Produced by a force acting at a distance, torque has direction given by the right hand rule and is treated as a vector (or axial vector) in physics.
Displacement: Represents directed distance from one point to another and is one of the simplest examples of a vector quantity.

Common Pitfalls:
Students sometimes confuse speed and velocity because their magnitudes can be numerically equal. The key difference is that velocity always includes direction, while speed does not. Another error is assuming that any quantity associated with motion is automatically a vector. The safer method is to ask whether the quantity must specify direction to be completely described. If direction is not needed, the quantity is scalar. This reasoning shows why speed is scalar and not a vector quantity.

Final Answer:
The quantity that is not a vector is Speed, which is a scalar with magnitude only.