Let
\begin{bmatrix} -0.5 \\ -0.5 \\ 0.5 \\ 0.5 \end{bmatrix}, \vec{v}_2 = \begin{bmatrix} 0.5 \\ -0.5 \\ -0.5 \\ 0.5 \end{bmatrix}, \vec{v}_3 = \begin{bmatrix} 0.5 \\ 0.5 \\ 0.5 \\ 0.5 \end{bmatrix}.
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 = \begin{bmatrix} \\\\\\ \end{bmatrix}
