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As shown in the diagram the points \(A\) and \(B\) have position vectors \(\mathbf { a }\) and \(\mathbf { b }\) with respect to the origin \(O\).
- Make a sketch of the diagram, and mark the points \(C , D\) and \(E\) such that \(\overrightarrow { O C } = 2 \mathbf { a } , \overrightarrow { O D } = 2 \mathbf { a } + \mathbf { b }\) and \(\overrightarrow { O E } = \frac { 1 } { 3 } \overrightarrow { O D }\).
- By expressing suitable vectors in terms of \(\mathbf { a }\) and \(\mathbf { b }\), prove that \(E\) lies on the line joining \(A\) and \(B\).