1. A straight road passes through villages at the points \(A\) and \(B\) with position vectors \(( 9 \mathbf { i } - 8 \mathbf { j } + 2 \mathbf { k } )\) and ( \(4 \mathbf { j } + \mathbf { k }\) ) respectively, relative to a fixed origin.

The road ends at a junction at the point \(C\) with another straight road which lies along the line with equation $$\mathbf { r } = ( 2 \mathbf { i } + 16 \mathbf { j } - \mathbf { k } ) + t ( - 5 \mathbf { i } + 3 \mathbf { j } ) ,$$ where \(t\) is a scalar parameter.

1. Find the position vector of \(C\). Given that 1 unit on each coordinate axis represents 200 metres,
2. find the distance, in kilometres, from the village at \(A\) to the junction at \(C\).