(Solved): Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the v ...

Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the vectors to produce an orthonormal set. \( u_{1}=\left[\begin{array}{r}\frac{2}{3} \\ \frac{1}{3} \\ -\frac{1}{3}\end{array}\right] \) and \( u_{2}=\left[\begin{array}{c}\frac{1}{3} \\ 0 \\ \frac{2}{3}\end{array}\right] \)