14 Three planes have equations
$$\begin{aligned}
k x - z & = 2
- x + k y + 2 z & = 1
2 k x + 2 y + 3 z & = 0
\end{aligned}$$
where \(k\) is a constant.
- By considering a suitable determinant, show that the three planes meet at a point for all values of \(k\).
- Using a matrix method, find, in terms of \(k\), the coordinates of the point of intersection of the planes.