7 The position vectors of points \(A , B\) and \(C\) relative to an origin \(O\) are given by
$$\overrightarrow { O A } = \left( \begin{array} { l }
2
1
3
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r }
6
- 1
7
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { l }
2
4
7
\end{array} \right)$$
- Show that angle \(B A C = \cos ^ { - 1 } \left( \frac { 1 } { 3 } \right)\).
- Use the result in part (i) to find the exact value of the area of triangle \(A B C\).