6 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations \(\mathbf { r } = - \mathbf { i } - 2 \mathbf { j } + \mathbf { k } + s ( 2 \mathbf { i } - 3 \mathbf { j } )\) and \(\mathbf { r } = 3 \mathbf { i } - 2 \mathbf { k } + t ( 3 \mathbf { i } - \mathbf { j } + 3 \mathbf { k } )\) respectively. The plane \(\Pi _ { 1 }\) contains \(l _ { 1 }\) and the point \(P\) with position vector \(- 2 \mathbf { i } - 2 \mathbf { j } + 4 \mathbf { k }\).

1. Find an equation of \(\Pi _ { 1 }\), giving your answer in the form \(\mathbf { r } = \mathbf { a } + \lambda \mathbf { b } + \mu \mathbf { c }\).
   The plane \(\Pi _ { 2 }\) contains \(l _ { 2 }\) and is parallel to \(l _ { 1 }\).
2. Find an equation of \(\Pi _ { 2 }\), giving your answer in the form \(\mathrm { ax } + \mathrm { by } + \mathrm { cz } = \mathrm { d }\).
3. Find the acute angle between \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\).
4. The point \(Q\) is such that \(\overrightarrow { \mathrm { OQ } } = - 5 \overrightarrow { \mathrm { OP } }\). Find the position vector of the foot of the perpendicular from the point \(Q\) to \(\Pi _ { 2 }\).