Orthogonality & Least Squares · Challenge problem

Two candidate planes model a signal $\mathbf b=(3,3,2)$: $W_1=\operatorname{span}\{(1,0,0),(0,1,0)\}$ and $W_2=\operatorname{span}\{(1,1,0),(1,-1,2)\}$. Whichever plane gives the SMALLER squared residual $\|\mathbf b-\operatorname{proj}_W\mathbf b\|^2$ is the better model. Find that smaller squared residual.