Another question that has a wrong answer from people adopting it. Am I wrong or the textbook wrong?
Answer from book:
My ans using the Gram-Schmidt process:
such that $\vec{x_1} and \vec{x_2}$ are the following respectively: 
$\vec{v_1}= \vec{x_1} = \begin{pmatrix}0\\ \:\:\:8\\ \:\:\:8\end{pmatrix}$
$\vec{v_2}= \vec{x_2} -(\frac{\vec{x_2}\cdot\vec{v_1}}{\vec{v_1}\cdot\vec{v_1}}) \vec{v_1}=\begin{pmatrix}4\\ \:\:\:7\\ \:\:\:3\end{pmatrix}-\frac{\left(\begin{pmatrix}4\\ \:\:7\\ \:\:3\end{pmatrix}\cdot \begin{pmatrix}0\\ \:\:8\\ \:\:8\end{pmatrix}\right)}{\begin{pmatrix}0\\ \:\:\:\:8\\ \:\:\:\:8\end{pmatrix}\cdot \begin{pmatrix}0\\ \:\:\:8\\ \:\:\:8\end{pmatrix}}\begin{pmatrix}0\\ \:\:\:\:8\\ \:\:\:\:8\end{pmatrix}=\begin{pmatrix}4\\ 2\\ -2\end{pmatrix}$