Introduction to Vectors and Scalars

Magnitude and Direction

Motion is the continuous change in the location of a particle or body. The amount of that change is called magnitude, while the change of position is direction.

A scalar is a measure of motion that considers only the magnitude, while a vector is a measure of motion that considers both magnitude and direction.

Consider the following examples of vectors and scalars.

Examples of Scalars

1. When a baseball player hits a triple, s/he runs around three bases. Each one is 90 feet apart. The total distance run is 3×90 or 270 feet.

This is a scalar measurement, since it ignores the direction and focuses solely on the magnitude or amount of the change in position. This scalar measurement is called distance.

2.  The baseball player in this example takes 15 seconds to run around the three bases. The rate of change in position in 270 feet/15 seconds, or 18 feet/second.

This is also a scalar measurement, since again it ignores the direction of the change of position. The scalar measurement of this rate of change is called speed.

Examples of Vectors

Using the same examples as above:

1. When the baseball player hits a triple, s/he runs from home plate to first to second and stops on third base. The distance between the starting point (home plate) and the ending point (third base) is 90 feet down the third base line.

This is a vector measurement, as it reflects both the magnitude (90 feet) of the change in position as well as the direction (down the third base line). This vector measurement is called displacement.

2. The baseball player took 15 seconds to run around the three bases and end up on third base. The rate of change in displacement is 90 feet/15 seconds, or 6 feet/second.

This is also a vector measurement, since (again) it considers both the change of position and the direction. The vector measurement of the change in displacement over time is called velocity.