Scalar and vector quantities

Scalars

Scalar quantities have only magnitude (size).

For example, 11 m and 15 m s-1 are both scalar quantities.

There are many scalar quantities:

Scalar quantities change when their magnitude changes.

Vectors

Vector quantities have both magnitude (size) and direction.

For example, 11 m east and 15 ms-1 at 30° to the horizontal are both vector quantities.

There are many vector quantities. This guide will use the following six:

Vector quantities change when:

  • their magnitude changes
  • their direction changes
  • their magnitude and direction both change

Example

A geostationary satellite is in orbit above the Earth. It moves at constant speed but its velocity is constantly changing (since its direction is always changing).

  • the difference in two scalar quantities = large value - small value
  • the difference in two vectors quantities = final vector - initial vector