4 The points \(A , B\) and \(C\) have position vectors \(\mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } , 2 \mathbf { i } + 4 \mathbf { j } + 5 \mathbf { k }\) and \(2 \mathbf { i } + 3 \mathbf { j } + 4 \mathbf { k }\) respectively. Find \(\overrightarrow { A B } \times \overrightarrow { A C }\).
Deduce, in either order, the exact value of
- the area of the triangle \(A B C\),
- the perpendicular distance from \(C\) to \(A B\).