9 With respect to the origin \(O\), the position vectors of the points \(A , B\) and \(C\) are given by
$$\overrightarrow { O A } = \left( \begin{array} { l }
0
5
2
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { l }
1
0
1
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { r }
4
- 3
- 2
\end{array} \right)$$
The midpoint of \(A C\) is \(M\) and the point \(N\) lies on \(B C\), between \(B\) and \(C\), and is such that \(B N = 2 N C\).
- Find the position vectors of \(M\) and \(N\).
- Find a vector equation for the line through \(M\) and \(N\).
- Find the position vector of the point \(Q\) where the line through \(M\) and \(N\) intersects the line through \(A\) and \(B\).