# vector equation of a line

Finding “real-life” examples at A-level is sometimes tricky. For an introduction to finding the vector equation of a line in Core 4 we considered the following picture.

The picture proved to be a great starting point for discussion as we considered how to describe the line through Bolt’s fingertips. We went on to discuss how the same line could be defined in a variety of ways;

- choosing different position vectors, e.g. Bolt’s elbow
- choosing a different direction vector
- standing somewhere different, and hence defining a new origin.

Whilst I was happy with the concept, I thought that it would be worth creating a more permanent resource.

## geogebra

Given the success of this as an introduction to vector equations of straight lines, I decided to make the following applet in geogebra: