The lines \(l_1\) and \(l_2\) have equations

\(\mathbf{r} = -2\mathbf{i} - 3\mathbf{j} - 5\mathbf{k} + \lambda(-4\mathbf{i} + 3\mathbf{j} + 5\mathbf{k})\) and \(\mathbf{r} = 2\mathbf{i} - 2\mathbf{j} + 3\mathbf{k} + \mu(2\mathbf{i} - 3\mathbf{j} + \mathbf{k})\)

respectively.

(a) Find the shortest distance between \(l_1\) and \(l_2\).

The plane \(\Pi\) contains \(l_1\) and the point with position vector \(-\mathbf{i} - 3\mathbf{j} - 4\mathbf{k}\).

(b) Find an equation of \(\Pi\), giving your answer in the form \(ax + by + cz = d\).