Find the orthogonal projection of $$\vec{v} = \left[\begin{array}{c} 0\cr 0\cr -2\cr 0 \end{array}\right]$$ onto the subspace $W$ of ${\mathbb R}^4$ spanned by $$\left[\begin{array}{c} -1\cr 1\cr -1\cr 1 \end{array}\right], \ \left[\begin{array}{c} 1\cr 1\cr 1\cr 1 \end{array}\right], \ \left[\begin{array}{c} -1\cr -1\cr 1\cr 1 \end{array}\right].$$
${\rm proj}_W(\vec{v})=$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$