Which one of the following is a vector quantity?

1. Analyze the question

The question asks us to identify which of the listed physical quantities is a vector quantity. To solve this, we must distinguish between scalar and vector quantities.

2. Explain the concept

• Scalar Quantities: These are physical quantities that have only magnitude (size) but no specific direction. Examples include mass, time, work, energy, distance, and temperature.
• Vector Quantities: These are physical quantities that have both magnitude and a specific direction. Examples include displacement, velocity, force, acceleration, and gradients (like temperature gradient or potential gradient).

3. Show the solution

Let's evaluate each option:

• B. Mass: Mass is a measure of the amount of matter in an object. It has magnitude (e.g., 5kg) but no direction. It is a scalar.
• C. Work: Work is defined as the product of force and displacement in the direction of the force. Even though it involves force and displacement (both vectors), the result of their dot product is a scalar. It has no direction. It is a scalar.
• D. Time: Time is a measure of duration. It has magnitude (e.g., 10 seconds) but does not have a direction. It is a scalar.
• A. Temperature gradient: A gradient represents the rate of change of a quantity with respect to distance. Because it indicates the direction in which the temperature changes most rapidly (from hot to cold), it possesses both magnitude and direction. Therefore, it is a vector.

4. Identify the answer

Based on the definitions above, the temperature gradient is the only vector quantity listed.

5. Tip

A simple way to remember vectors is the acronym "FAT VED": Force, Acceleration, Torque, Velocity, Electric field, and Displacement. If a quantity is a "gradient" of a scalar field, it is almost always a vector!