Orthogonality & Least Squares · Challenge problem

The vectors $\mathbf u=(1,2,2)$, $\mathbf v=(2,-2,1)$, $\mathbf w=(2,1,-2)$ are pairwise orthogonal. A measured vector $\mathbf b=(7,-2,10)$ is written as $\mathbf b = x\mathbf u+y\mathbf v+z\mathbf w$. Find $x^2+y^2+z^2$.