1 The points \(A , B\) and \(C\) have position vectors \(\mathbf { a } = \left( \begin{array} { l } 1
1
3 \end{array} \right) , \mathbf { b } = \left( \begin{array} { r } 2
3
- 1 \end{array} \right)\) and \(\mathbf { c } = \left( \begin{array} { r } - 5
1
2 \end{array} \right)\) respectively, relative to the origin \(O\).

1. Calculate, in its simplest exact form, the area of triangle \(O A B\).
2. Show that \(\mathbf { a } \times ( \mathbf { b } \times \mathbf { c } ) + \mathbf { b } \times ( \mathbf { c } \times \mathbf { a } ) + \mathbf { c } \times ( \mathbf { a } \times \mathbf { b } ) = \mathbf { 0 }\).