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. (a) Find an equation of \(\Pi_1\), giving your answer in the form \(\mathbf{r} = \mathbf{a} + \lambda \mathbf{b} + \mu \mathbf{c}\).
2. (b) The plane \(\Pi_2\) contains \(l_2\) and is parallel to \(l_1\). Find an equation of \(\Pi_2\), giving your answer in the form \(ax + by + cz = d\).
3. (c) Find the acute angle between \(\Pi_1\) and \(\Pi_2\).
4. (d) The point \(Q\) is such that \(\overrightarrow{OQ} = -5\overrightarrow{OP}\). Find the position vector of the foot of the perpendicular from the point \(Q\) to \(\Pi_2\).