10 Three planes have equations
$$\begin{aligned}
- x + 2 y + z & = 0
2 x - y - z & = 0
x + y & = a
\end{aligned}$$
where \(a\) is a constant.
- Investigate the arrangement of the planes:
- when \(a = 0\);
- when \(a \neq 0\).
- Chris claims that the position vectors \(- \mathbf { i } + 2 \mathbf { j } + \mathbf { k } , 2 \mathbf { i } - \mathbf { j } - \mathbf { k }\) and \(\mathbf { i } + \mathbf { j }\) lie in a plane. Determine whether or not Chris is correct.