Orthogonality & Least Squares · Hard problem

Apply Gram–Schmidt to $\mathbf u = (1, 4, -3)$, $\mathbf v = (-4, -2, 0)$ (in that order, without normalizing). Find the second vector $\mathbf w_2 = \mathbf v - \operatorname{proj}_{\mathbf u}\mathbf v$.