Orthogonality & Least Squares · Medium problem

A signal $\mathbf b=(1,2,2)$ can be filtered onto either the plane $W_1=\operatorname{span}\{(1,0,0),(0,1,0)\}$ or the plane $W_2=\operatorname{span}\{(1,1,0),(0,0,1)\}$. Whichever plane keeps more of the signal's energy (the larger $\|\operatorname{proj}_W\mathbf b\|^2$) is the better filter. Find that larger value.