7. The plane \(\Pi _ { 1 }\) has equation \(x + y + z = 3\) and the plane \(\Pi _ { 2 }\) has equation \(2 x + 3 y - z = 4\) The planes \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\) intersect in the line \(L\).
- Find a cartesian equation for the line \(L\).
The plane \(\Pi _ { 3 }\) has equation
$$\text { r. } \left( \begin{array} { r }
5
- 4
4
\end{array} \right) = 12$$
The line \(L\) meets the plane \(\Pi _ { 3 }\) at the point \(A\). - Find the coordinates of \(A\).
- Find the acute angle between \(\overrightarrow { O A }\) and the line \(L\), where \(O\) is the origin. Give your answer in degrees to one decimal place.