## Table of Contents

## Scalar Quantities

**Scalar quantities** are quantities in which the magnitude is stated, but the direction is either not applicable or not specified.

**Examples:**

- Length
- Volume
- Mass
- Speed

## Vector Quantities

**Vector quantities** are quantities in which both the magnitude and the direction must be stated.

**Examples:**

- Force
- Velocity
- Displacement
- Acceleration

It does not make sense to say that you’re applying a force of 10 N on a box without stating the direction. The force can be directed anywhere. Hence, you need to specify which direction the force is applied: 10 N in the horizontal direction on a box.

There will be more about how to differentiate speed, displacement, velocity and acceleration in the later chapter.

## Worked Examples

### Example 1

Which one of the following groups contains only vector quantities?

- force, work, energy
- displacement, momentum, acceleration
- power, energy, time
- momentum, mass, velocity

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Vector quantities: Force, displacement, momentum, velocity, acceleration

Scalar quantities: Work, energy, power, time, mass

Answer: 2

### Example 2

Which of the following are vectors and which are not: force, temperature, the volume of water in a can, the ratings of a TV show, the height of a building, the velocity of a sports car, the age of the Universe?

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Only force and velocity are vectors. None of the other quantities requires a direction to be described.

### Example 3

Can the magnitude of a vector have a negative value?

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No, the magnitude of a vector is always positive. A minus sign in a vector only indicates direction, not magnitude.

### Example 4

Is it possible to add a vector quantity to a scalar quantity? Explain.

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Addition of a vector to a scalar is not defined.