Chapter 2: Vectors

2.1 What is a vector?

A vector is a quantity with a magnitude (size) and direction. A quantity with only a magnitude is called a scalar.

For example, speed is a scalar quantityâ€”it tells you how quickly something is moving, but gives no indication of direction. If you tell someone “I am driving at 42 miles per hour,” you are telling them your speed.

If you tell someone “I am driving 42 miles per hour to the East,” you have told them how fast you’re going and what direction you’re moving. These two pieces of information together give you a vector quantity. (The quantity that gives information about both speed and direction of motion is called velocity. You’ll learn more about this in chapter 4.)

Example 2.1

Temperature is a scalar quantity. It tells you how hot or cold something is.

Example 2.2

A force can be thought of as a push or a pull in some direction. Force is a vector, because it includes information about direction. (You’ll learn more about forces in chapter 9.)