CHAPTER 9

A Bit About Vectors

IN THIS CHAPTER
Summary: Understand the difference between scalars and vectors, how to draw vectors, how to break down vectors into components, and
how to add vectors.

Key Ideas
Scalars are quantities that have a magnitude but no direction—for example, temperature; in contrast,
vectors have both magnitude and direction—for example, velocity.
Vectors are drawn as arrows; the length of the arrow corresponds to the magnitude of the vector, and
the direction of the arrow represents the direction of the vector.
Any vector can be broken down into its x - and y -components; breaking a vector into its components
will make many problems simpler.

Relevant Equations

Note: this assumes that θ is measured from the horizontal. These equations are not on the equation sheet,
but should be memorized.

Scalars and vectors are easy. So we’ll make this quick.

Scalars

Scalars are numbers that have a magnitude but no direction.

Magnitude: How  big something   is

For example, temperature is a scalar. On a cold winter day, you might say that it is “4 degrees” outside.
The units you used were “degrees.” But the temperature was not oriented in a particular way; it did not
have a direction.