The lines l and m have vector equations

\(\mathbf{r} = \mathbf{i} - 2\mathbf{k} + s(2\mathbf{i} + \mathbf{j} + 3\mathbf{k})\)

and

\(\mathbf{r} = 6\mathbf{i} - 5\mathbf{j} + 4\mathbf{k} + t(\mathbf{i} - 2\mathbf{j} + \mathbf{k})\)

respectively.

Show that l and m intersect, and find the position vector of their point of intersection.