6 Relative to the origin \(O\), the points \(A , B\) and \(C\) have position vectors given by
$$\overrightarrow { O A } = \left( \begin{array} { l }
1
3
1
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { l }
3
1
2
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { r }
5
3
- 2
\end{array} \right)$$
- Using a scalar product, find the cosine of angle \(B A C\).
- Hence find the area of triangle \(A B C\). Give your answer in a simplified exact form.