Enter exact coefficients below. Do not round.
\[\vec {x}=\answer {-2/\sqrt {2}}\vec {q}_1+\answer {6/\sqrt {3}}\vec {q}_2\]
Vectors \(\vec {q}_1=\frac {1}{\sqrt {2}}\begin{bmatrix}1\\1\\0\end{bmatrix}\) and \(\vec {q}_2=\frac {1}{\sqrt {3}}\begin{bmatrix}1\\-1\\1\end{bmatrix}\) form an orthonormal basis for the plane \(x-y-2z=0\). (You should know how to
verify that \(\vec {q}_1\), \(\vec {q}_2\) are orthonormal.) Use orthogonal projections to express \(\vec {x}=\begin{bmatrix}1\\-3\\2\end{bmatrix}\) as a linear
combination of \(\vec {q}_1\) and \(\vec {q}_2\).