- Relative to a fixed origin, points \(P , Q\) and \(R\) have position vectors \(\mathbf { p } , \mathbf { q }\) and \(\mathbf { r }\) respectively.
Given that
- \(\quad P , Q\) and \(R\) lie on a straight line
- \(Q\) lies one third of the way from \(P\) to \(R\)
show that
$$\mathbf { q } = \frac { 1 } { 3 } ( \mathbf { r } + 2 \mathbf { p } )$$