9 The lines \(l\) and \(m\) have vector equations $$\mathbf { r } = 2 \mathbf { i } - \mathbf { j } + 4 \mathbf { k } + s ( \mathbf { i } + \mathbf { j } - \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = - 2 \mathbf { i } + 2 \mathbf { j } + \mathbf { k } + t ( - 2 \mathbf { i } + \mathbf { j } + \mathbf { k } )$$ respectively.

1. Show that \(l\) and \(m\) do not intersect. The point \(P\) lies on \(l\) and the point \(Q\) has position vector \(2 \mathbf { i } - \mathbf { k }\).
2. Given that the line \(P Q\) is perpendicular to \(l\), find the position vector of \(P\).
3. Verify that \(Q\) lies on \(m\) and that \(P Q\) is perpendicular to \(m\).