7 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have vector equations
$$\mathbf { r } = 4 \mathbf { i } - 2 \mathbf { j } + \lambda ( 2 \mathbf { i } + \mathbf { j } - 4 \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = 4 \mathbf { i } - 5 \mathbf { j } + 2 \mathbf { k } + \mu ( \mathbf { i } - \mathbf { j } - \mathbf { k } )$$
respectively.
- Show that \(l _ { 1 }\) and \(l _ { 2 }\) intersect.
- Find the perpendicular distance from the point \(P\) whose position vector is \(3 \mathbf { i } - 5 \mathbf { j } + 6 \mathbf { k }\) to the plane containing \(l _ { 1 }\) and \(l _ { 2 }\).
- Find the perpendicular distance from \(P\) to \(l _ { 1 }\).