Orthogonality & Least Squares · Medium problem

A triangular frame is in equilibrium only if the sum of its three strut forces is orthogonal to the frame's out-of-plane normal $\mathbf n = (1,1,1)$. Two of the strut forces are $\mathbf f_1 = (2,-1,0)$ and $\mathbf f_2 = (-1,3,-1)$. Find the magnitude of the out-of-plane imbalance – the projection of $\mathbf f_1+\mathbf f_2$ onto $\mathbf n$ – that the third strut must cancel.