Scientists often make measurements. The physical quantities they measure fall into two categories: scalars and vectors. Scalar and vector quantities are treated differently in calculations.

Vector quantities have both magnitude and an associated direction. This makes them different from scalar quantities, which just have magnitude.

Some examples of vector quantities include:

- force ā eg 20 newtons (N) to the left
- weight ā eg 600 newtons (N) downwards
- displacement ā eg 50 kilometres (km) east
- velocity ā eg 11 metres per second (m/s) upwards
- acceleration ā eg 9.8 metres per second squared (m/s
^{2}) downwards - momentum ā eg 250 kilogram metres per second (kg m/s) south west

The direction of a vector can be given in a written description, or drawn as an arrow. The length of an arrow represents the magnitude of the quantity. If one arrow is twice as long as another, it represents a force which has twice the magnitude.

The diagrams show three examples of vectors, drawn to different scales.