12.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8b616e3c-db87-430e-91c1-63a24e2f9593-26_390_630_351_721}
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\caption{Diagram NOT accurately drawn}
\end{figure}
The diagram shows a quadrilateral \(O A C B\) in which
$$\overrightarrow { O A } = 4 \mathbf { a } \quad \overrightarrow { O B } = 3 \mathbf { b } \quad \overrightarrow { B C } = 2 \mathbf { a } + \mathbf { b }$$
The point \(P\) lies on \(A C\) such that \(A P : P C = 3 : 2\)
The point \(Q\) is such that \(O P Q\) and \(B C Q\) are straight lines.
Using a vector method, find \(\overrightarrow { O Q }\) in terms of \(\mathbf { a }\) and \(\mathbf { b }\)
Give your answer in its simplest form.
Show your working clearly.