6 The points \(A\) and \(B\) have position vectors \(\mathbf { a } = \mathbf { i } + 2 \mathbf { j } + \mathbf { k }\) and \(\mathbf { b } = - 3 \mathbf { i } + 4 \mathbf { j } - 5 \mathbf { k }\) respectively.
- Determine the area of triangle \(O A B\), giving your answer in an exact form.
The point \(C\) lies on the line \(( \mathbf { r } - \mathbf { a } ) \times ( \mathbf { b } - \mathbf { a } ) = \mathbf { O }\) such that the area of triangle \(O A C\) is half the area of triangle \(O A B\).
- Determine the two possible position vectors of \(C\).