Orthogonality & Least Squares · Hard problem

Apply Gram–Schmidt (without normalizing) to $\mathbf v_1 = (1, 1, 1, 1)$, $\mathbf v_2 = (1, 1, 0, 0)$, $\mathbf v_3 = (1, 0, 0, 0)$, in that order, producing $\mathbf w_1, \mathbf w_2, \mathbf w_3$. Find $\|\mathbf w_3\|$.