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Determine the position vector of $M$. Write your answer in terms of $\mathbf a$ and $\mathbf b$, and simplify it fully.
Mathematics 0580 · IGCSE · Vectors in two dimensions
Vectors in two dimensions — practice question
The diagram indicates that $OBD$ and $ACD$ are straight lines. $O$ is the origin, the position vector of $A$ is $\mathbf a$ and the position vector of $B$ is $\mathbf b$. $\overrightarrow{BC}=\frac13\overrightarrow{OA}$. $M$ is located at the midpoint of $CD$.