Vector quantities

Vector quantities have size or magnitude as well as an associated direction. This makes them different from scalar quantities, which only have a size or magnitude.

Examples of vector quantities

Some examples of vector quantities that refer to motion include:

  • displacement, eg 50 kilometres (50 km) east
  • velocity, eg 11 metres per second (11 m/s) upwards

Notice how the quantities above have both a size and a direction associated with them.

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.

Three different arrows pointing in different directions, the first to the left 20 N, another to the right labelled 50 km and the third pointing downwards, labelled 9.8 m/s2.

Displacement and average velocity example

Displacement is the overall distance from a fixed point. Average velocity is the total displacement divided by time.

If an athlete runs 400 m north before turning back and running 400 m south at the same speed, their overall displacement is 0 m. Although the athlete has run 800 m in total, their final distance from the starting point is 0 m as they have returned to the start.

The average velocity of the athlete is also 0 m/s, due to the fact that their displacement is 0 m. If the athlete runs at a velocity of v m/s in one direction, then their velocity in the opposite direction must be -v m/s. These two values cancel each other out, giving 0 m/s overall.