Let $$\vec{u} = \left[\begin{array}{c} 0\cr -1\cr 2\cr -1 \end{array}\right], \vec{v} = \left[\begin{array}{c} -1\cr -3\cr 3\cr 4 \end{array}\right],$$ and let $W$ the subspace of ${\mathbb R}^4$ spanned by $\vec{u}$ and $\vec{v}$. Find a basis of $W^{\perp}$, the orthogonal complement of $W$ in $\mathbb{R}^4$.

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