10 With respect to the origin \(O\), the points \(A\) and \(B\) have position vectors given by \(\overrightarrow { O A } = 6 \mathbf { i } + 2 \mathbf { j }\) and \(\overrightarrow { O B } = 2 \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k }\). The midpoint of \(O A\) is \(M\). The point \(N\) lying on \(A B\), between \(A\) and \(B\), is such that \(A N = 2 N B\).

1. Find a vector equation for the line through \(M\) and \(N\).
   The line through \(M\) and \(N\) intersects the line through \(O\) and \(B\) at the point \(P\).
2. Find the position vector of \(P\).
3. Calculate angle \(O P M\), giving your answer in degrees.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.