6 The points \(A , B\) and \(C\) have coordinates \(( 3 , - 2,4 ) , ( 1 , - 5,6 )\) and \(( - 4,5 , - 1 )\) respectively. The line \(l\) passes through \(A\) and has equation \(\mathbf { r } = \left[ \begin{array} { r } 3
- 2
4 \end{array} \right] + \lambda \left[ \begin{array} { r } 7
- 7
5 \end{array} \right]\).

1. Show that the point \(C\) lies on the line \(l\).
2. Find a vector equation of the line that passes through points \(A\) and \(B\).
3. The point \(D\) lies on the line through \(A\) and \(B\) such that the angle \(C D A\) is a right angle. Find the coordinates of \(D\).
4. The point \(E\) lies on the line through \(A\) and \(B\) such that the area of triangle \(A C E\) is three times the area of triangle \(A C D\). Find the coordinates of the two possible positions of \(E\).