Answer
Geometrically, the solution set is the line through$\left[\begin{array}{ r }5\\-2\\0\end{array}\right]\text{ in the direction of }\left[\begin{array}{ r }4\\-7\\1\end{array}\right].$
Work Step by Step
To write the general solution in parametric vector form, pull out the constant terms that do not involve the free variable:
$x=\left[\begin{array}{ l }x_1\\x_2\\x_3\end{array}\right]=\left[\begin{array}{ c }5+4x_3\\-2-7x_3\\x_3\end{array}\right]=\left[\begin{array}{ r }5\\-2\\0\end{array}\right]+\left[\begin{array}{ r }4x_3\\-7x_3\\x_3\end{array}\right]=\left[\begin{array}{ r }5\\-2\\0\end{array}\right]+x_3\left[\begin{array}{ r }4\\-7\\1\end{array}\right]$
$=p+x_3q$
Geometrically, the solution set is the line through$\left[\begin{array}{ r }5\\-2\\0\end{array}\right]\text{ in the direction of }\left[\begin{array}{ r }4\\-7\\1\end{array}\right].$
