7 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations \(\mathbf { r } = - 5 \mathbf { j } + \lambda ( 5 \mathbf { i } + 2 \mathbf { k } )\) and \(\mathbf { r } = 4 \mathbf { i } + 2 \mathbf { j } - 2 \mathbf { k } + \mu ( \mathbf { j } + \mathbf { k } )\) respectively. The plane \(\Pi\) contains \(l _ { 1 }\) and is parallel to \(l _ { 2 }\).

1. Find the equation of \(\Pi\), giving your answer in the form \(a x + b y + c z = d\).
2. Find the distance between \(l _ { 2 }\) and \(\Pi\).
   The point \(P\) on \(l _ { 1 }\) and the point \(Q\) on \(l _ { 2 }\) are such that \(P Q\) is perpendicular to both \(l _ { 1 }\) and \(l _ { 2 }\).
3. Show that \(P\) has position vector \(\frac { 55 } { 27 } \mathbf { i } - 5 \mathbf { j } + \frac { 22 } { 27 } \mathbf { k }\) and state a vector equation for \(P Q\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.