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

(a) Find a unit vector in the direction of l.

The line m passes through the points A and B.

(b) Find a vector equation for m.

(c) Determine whether lines l and m are parallel, intersect or are skew.