7 Two lines have vector equations $$\mathbf { r } = \mathbf { i } - 2 \mathbf { j } + 4 \mathbf { k } + \lambda ( 3 \mathbf { i } + \mathbf { j } + a \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = - 8 \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } + \mu ( \mathbf { i } - 2 \mathbf { j } - \mathbf { k } ) ,$$ where \(a\) is a constant.

1. Given that the lines are skew, find the value that \(a\) cannot take.
2. Given instead that the lines intersect, find the point of intersection.