0606 P12 - Jun 2025 - Q11 - 9 marks
7125
The diagram shows the triangle \(OAB\), where \(\overrightarrow{OA}=\mathbf{a}\) and \(\overrightarrow{OB}=\mathbf{b}\).
The point \(P\) lies on \(OA\) such that \(\overrightarrow{OP}=\frac34\overrightarrow{OA}\).
The point \(Q\) lies on \(AB\) such that \(\overrightarrow{AQ}=\frac13\overrightarrow{AB}\).
The straight line through \(P\) and \(Q\) meets the straight line through \(O\) and \(B\) at the point \(R\). It is given that \(\overrightarrow{OR}=\lambda\mathbf{b}\) and \(\overrightarrow{PR}=\mu\overrightarrow{PQ}\), where \(\lambda\) and \(\mu\) are constants.
(a) Find \(\overrightarrow{OR}\) in terms of \(\mathbf{a}\), \(\mathbf{b}\) and \(\mu\).
(b) Hence find the values of \(\lambda\) and \(\mu\).
