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Find the position vector of $S$ in terms of $\mathbf{p}$ and $\mathbf{q}$. Give the answer in its simplest form.
Mathematics 0580 · IGCSE · Vector geometry
Vector geometry — practice question
In the diagram, $O$ marks the origin. $\overrightarrow{OP} = \mathbf{p}$ and $\overrightarrow{OQ} = \mathbf{q}$. $R$ is where $PQ$ meets $OS$, with $PR : RQ = 1 : 2$ and $OR = RS$. The diagram is not drawn to scale.