Relative to a fixed origin \(O\), the point \(A\) has position vector \(\mathbf { i } - 3 \mathbf { j } + 2 \mathbf { k }\) and the point \(B\) has position vector \(- 2 \mathbf { i } + 2 \mathbf { j } - \mathbf { k }\). The points \(A\) and \(B\) lie on a straight line \(l\).
Find \(\overrightarrow { A B }\).
Find a vector equation of \(l\).
The point \(C\) has position vector \(2 \mathbf { i } + p \mathbf { j } - 4 \mathbf { k }\) with respect to \(O\), where \(p\) is a constant. Given that \(A C\) is perpendicular to \(l\), find