Vectors tell us both size (magnitude) and direction. It helps to describe movement between points.

Scalars can only tell us magnitude.

Vectors can be shown with a straight line and an arrow to show the direction, as shown below. To describe the vector between A and B, we write it as: \overset { \rightarrow }{ AB }

We can also represent a vector using columns: (\begin{matrix} 3 \ 4 \end{matrix})</span>. The top number shows how many times you move to along the x axis and the bottom number shows how many times you move along the y axis. In this example, to get from A to B, we move along the x axis 3 spaces and up the y axis 4 spaces.

  • If the numbers are negative, that means you go to the left or down.
  • A negative vector is one that is going backwards.

Below is an example of how to add vectors:

This method is used for subtracting vectors too.

Solving geometric problems

Look at the diagram below, to find \overset { \rightarrow }{ KM }, you have to do \overset { \rightarrow }{ KO } +\overset { \rightarrow }{ OM } which is the same as writing -a+b or b-a.