10 The points \(A\) and \(B\) have position vectors \(2 \mathbf { i } + \mathbf { j } + \mathbf { k }\) and \(\mathbf { i } - 2 \mathbf { j } + 2 \mathbf { k }\) respectively. The line \(l\) has vector equation \(\mathbf { r } = \mathbf { i } + 2 \mathbf { j } - 3 \mathbf { k } + \mu ( \mathbf { i } - 3 \mathbf { j } - 2 \mathbf { k } )\).
- Find a vector equation for the line through \(A\) and \(B\).
- Find the acute angle between the directions of \(A B\) and \(l\), giving your answer in degrees.
- Show that the line through \(A\) and \(B\) does not intersect the line \(l\).