9 The points \(A\) and \(B\) have position vectors \(\mathbf { i } + 2 \mathbf { j } - \mathbf { k }\) and \(3 \mathbf { i } + \mathbf { j } + \mathbf { k }\) respectively. The line \(l\) has equation \(\mathbf { r } = 2 \mathbf { i } + \mathbf { j } + \mathbf { k } + \mu ( \mathbf { i } + \mathbf { j } + 2 \mathbf { k } )\).
- Show that \(l\) does not intersect the line passing through \(A\) and \(B\).
- The plane \(m\) is perpendicular to \(A B\) and passes through the mid-point of \(A B\). The plane \(m\) intersects the line \(l\) at the point \(P\). Find the equation of \(m\) and the position vector of \(P\).