7 Three planes have equations
$$\begin{array} { r }
x + 2 y - 3 z = 0
- x + 3 y - 2 z = 0
x - 2 y + k z = k
\end{array}$$
where \(k\) is a constant.
- For the case \(k = 0\), the origin lies on all three planes.
Use a determinant to explain whether there are any other points that lie on all three planes in this case.
- You are now given that \(k = 1\).
- Show that there are no points that lie on all three planes.
- Describe the geometrical arrangement of the three planes.