Let $$\vec{v}_1 = \left[\begin{array}{c} 0.5\cr -0.5\cr -0.5\cr -0.5 \end{array}\right], \ \vec{v}_2 = \left[\begin{array}{c} 0.5\cr -0.5\cr 0.5\cr 0.5 \end{array}\right], \ \vec{v}_3 = \left[\begin{array}{c} 0.5\cr 0.5\cr 0.5\cr -0.5 \end{array}\right].$$ Find a vector $\vec{v}_4$ in ${\mathbb R}^4$ such that the vectors $\vec{v}_1$, $\vec{v}_2$, $\vec{v}_3$, and $\vec{v}_4$ are orthonormal.

$\vec{v}_4=$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$