Orthogonality & Least Squares · Hard problem

Apply Gram–Schmidt to $\mathbf u = (-2, 2, 2)$, $\mathbf v = (3, -1, 4)$ (in that order, without normalizing). Find the second vector $\mathbf w_2 = \mathbf v - \operatorname{proj}_{\mathbf u}\mathbf v$.