(a) Given that \(a\) is an integer, show that the system of equations
\(\begin{aligned} a x+3 y+z & =14 \\ 2 x+y+3 z & =0 \\ -x+2 y-5 z & =17 \end{aligned}\)
has a unique solution and interpret this situation geometrically.
(b) Find the value of \(a\) for which \(x=1, y=4, z=-2\) is the solution to the system of equations in part (a).