9 Points \(A , B\) and \(C\) have position vectors \(\mathbf { a } , \mathbf { b }\) and \(\mathbf { c }\) relative to an origin \(O\) in 3-dimensional space. Rectangles \(O A D C\) and \(B E F G\) are the base and top surface of a cuboid.
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- The point \(M\) is the midpoint of \(B C\).
- The point \(X\) lies on \(A M\) such that \(A X = 2 X M\).
- Find \(\overrightarrow { O X }\) in terms of \(\mathbf { a } , \mathbf { b }\) and \(\mathbf { c }\), simplifying your answer.
- Hence show that the lines \(O F\) and \(A M\) intersect.