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Find the position vector of $M$. Express your answer in terms of $\mathbf{a}$ and $\mathbf{b}$, and simplify it fully.
Mathematics 0580 · IGCSE · Vector geometry
Vector geometry — practice question
In the diagram, $OA$ runs 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 $\mathbf{b}$.