1 The points \(A , B\) and \(C\) have position vectors \(6 \mathbf { i } + 2 \mathbf { j } + 4 \mathbf { k } , 13 \mathbf { i } + 2 \mathbf { j } + 5 \mathbf { k }\) and \(16 \mathbf { i } + 6 \mathbf { j } + 3 \mathbf { k }\) respectively.

1. Using the vector product, calculate the area of triangle \(A B C\).
2. Hence find, in simplest surd form, the perpendicular distance from \(C\) to the line through \(A\) and \(B\).