\(ABCDEFGH\) is a regular octagon. Express in terms of a single vector the sum of the vectors

  1. \(\mathbf{AC},\mathbf{AH},\mathbf{HG}\),

We can start by choosing one convenient pair to add. Remember that as long as we keep the sense correct we can add them in whatever order we like.

Given that \(\big \vert \mathbf{AB} \big \vert = 2,\) calculate \(\big \vert \mathbf{AF} \big \vert\).

What can we say about the lines \(AF\) and \(GH\)?