Find the cartesian equation of the plane through the point ( \(2 , - 1,4\) ) with normal vector
$$\mathbf { n } = \left( \begin{array} { r }
1
- 1
2
\end{array} \right)$$
Find the coordinates of the point of intersection of this plane and the straight line with equation
$$\mathbf { r } = \left( \begin{array} { r }
7
12
9
\end{array} \right) + \lambda \left( \begin{array} { l }
1
3
2
\end{array} \right)$$