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.
Find the value of \(a\) for which \(x = 1 , y = 4 , z = - 2\) is the solution to the system of equations in part (a).