The plane \(\Pi\) has equation \(\mathbf{r} = 2\mathbf{i} + 3\mathbf{j} - 2\mathbf{k} + \lambda (\mathbf{i} - 2\mathbf{j} - \mathbf{k}) + \mu (3\mathbf{i} + 2\mathbf{j} - 2\mathbf{k})\).

(a) Find a Cartesian equation of \(\Pi\), giving your answer in the form \(ax + by + cz = d\).

The point \(P\) has position vector \(4\mathbf{i} + 2\mathbf{j} + 9\mathbf{k}\).

(b) Find the position vector of the foot of the perpendicular from \(P\) to \(\Pi\).

The line \(l\) is parallel to the vector \(3\mathbf{i} + 5\mathbf{j} - \mathbf{k}\).

(c) Find the acute angle between \(l\) and \(\Pi\).