7 Relative to an origin \(O\), the position vectors of the points \(A , B\) and \(C\) are given by $$\overrightarrow { O A } = \left( \begin{array} { r } 1
- 3
2 \end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r } - 1
3
5 \end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { r } 3
1
- 2 \end{array} \right)$$

1. Find \(\overrightarrow { A C }\).
2. The point \(M\) is the mid-point of \(A C\). Find the unit vector in the direction of \(\overrightarrow { O M }\).
3. Evaluate \(\overrightarrow { A B } \cdot \overrightarrow { A C }\) and hence find angle \(B A C\).