The points A and B have position vectors \(2\mathbf{i} + \mathbf{j} + \mathbf{k}\) and \(\mathbf{i} - 2\mathbf{j} + 2\mathbf{k}\) respectively. The line \(l\) has vector equation \(\mathbf{r} = \mathbf{i} + 2\mathbf{j} - 3\mathbf{k} + \mu(\mathbf{i} - 3\mathbf{j} - 2\mathbf{k})\).

(a) Find a vector equation for the line through A and B.

(b) Find the acute angle between the directions of \(AB\) and \(l\), giving your answer in degrees.

(c) Show that the line through A and B does not intersect the line \(l\).