In the diagram, \(OA\) is parallel to \(BC\).
\(BC=3OA\)
\(M\) is the midpoint of \(AC\).
The position vector of \(A\) is \(\mathbf a\) and the position vector of \(B\) is \(\mathbf b\).
Find the position vector of \(M\).
Give your answer in terms of \(\mathbf a\) and \(\mathbf b\), in its simplest form.[3]
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