Enter exact coefficients below. Do not round.
\[\vec {x}=\answer {19}\vec {q}_1+\answer {21/\sqrt {10}}\vec {q}_2\]
Vectors \(\vec {q}_1=\frac {1}{7}\begin{bmatrix}2\\-3\\6\end{bmatrix}\) and \(\vec {q}_2=\frac {1}{\sqrt {10}}\begin{bmatrix}3\\0\\-1\end{bmatrix}\) form an orthonormal basis for the plane \(3x+20y+9z=0\). (You should know how to
verify that \(\vec {q}_1\), \(\vec {q}_2\) are orthonormal.) Express the orthogonal projection of \(\vec {x}=\begin{bmatrix}14\\7\\21\end{bmatrix}\) onto the plane
as a linear combination of \(\vec {q}_1\) and \(\vec {q}_2\).