In the diagram, $$\(O A\)$$ is parallel to $$\(B C\)$$. DO NOT WRITE IN THIS MARGIN $$\(B C=3 O A\)$$ $$\(M\)$$ is the midpoint of $$\(A C\)$$. The position vector of $$\(A\)$$ is a and the position vector of $$\(B\)$$ is $$\(\mathbf{b}\)$$. Find the position vector of $$\(M\)$$. Give your answer in terms of $$\(\mathbf{a}\)$$ and $$\(\mathbf{b}\)$$, in its simplest form. DO NOT WRITE IN THIS MARGIN ............................................. DO NOT WRITE IN THIS MARGIN

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