5 The plane \(\Pi\) has equation \(\mathbf { r } = - 2 \mathbf { i } + 3 \mathbf { j } + 3 \mathbf { k } + \lambda ( \mathbf { i } + \mathbf { k } ) + \mu ( 2 \mathbf { i } + 3 \mathbf { j } )\).
- Find a Cartesian equation of \(\Pi\), giving your answer in the form \(a x + b y + c = d\).
The line \(l\) passes through the point \(P\) with position vector \(2 \mathbf { i } - 3 \mathbf { j } + 5 \mathbf { k }\) and is parallel to the vector \(\mathbf { k }\). - Find the position vector of the point where \(l\) meets \(\Pi\).
- Find the acute angle between \(l\) and \(\Pi\).
- Find the perpendicular distance from \(P\) to \(\Pi\).