Find the cross products \(\mathbf{u} \times \mathbf{v}\) and \(\mathbf{v} \times \mathbf{u}\) for the vectors \(\mathbf{u} = \langle 3, 4, 0 \rangle\) and \(\mathbf{v} = \langle 0, 2, -4 \rangle\).
\(\mathbf{u} \times \mathbf{v} = \boxed{} \mathbf{i} + \boxed{} \mathbf{j} + \boxed{} \mathbf{k}\) (Simplify your answers.)