Orthogonality & Least Squares · Hard problem

A noise-filtering system in $\mathbb R^3$ keeps only the component of an incoming signal lying in the plane spanned by $(1,1,0)$ and $(0,1,1)$ (the two spanning directions are not orthogonal). For the signal $\mathbf s = (2,-1,3)$, find the fraction of its energy ($\|\mathbf s\|^2$) that survives the filter, i.e. $\dfrac{\|\operatorname{proj}_W\mathbf s\|^2}{\|\mathbf s\|^2}$.