2025 IGCSE 0580 October/November P21 Q24

In the diagram, \(OBD\) and \(ACD\) are straight lines.

\(O\) is the origin, the position vector of \(A\) is \(\mathbf a\) and the position vector of \(B\) is \(\mathbf b\).

\(\overrightarrow{BC}=\dfrac13\overrightarrow{OA}\)

\(M\) is the midpoint of \(CD\).

Find the position vector of \(M\).

Give your answer in terms of \(\mathbf a\) and \(\mathbf b\), in its simplest form.[4]