May/June 2026 Paper 23

In the diagram, $O$ is the origin, $\overrightarrow{OR}=\mathbf{r}$ and $\overrightarrow{OS}=\mathbf{s}$. $P$ is a point on $RS$ and $RP:PS=2:5$.

Find the position vector of $P$. Give your answer, in terms of $\mathbf{r}$ and $\mathbf{s}$, in its simplest form.