6 The plane \(\Pi\) has equation \(\mathbf { r } = \left( \begin{array} { l } 1
6
7 \end{array} \right) + \lambda \left( \begin{array} { r } 2
- 1
- 1 \end{array} \right) + \mu \left( \begin{array} { r } 2
- 3
- 5 \end{array} \right)\) and the line \(l\) has equation \(\mathbf { r } = \left( \begin{array} { l } 7
4
1 \end{array} \right) + t \left( \begin{array} { r } 3
0
- 1 \end{array} \right)\).

1. Express the equation of \(\Pi\) in the form r.n \(= p\).
2. Find the point of intersection of \(l\) and \(\Pi\).
3. The equation of \(\Pi\) may be expressed in the form \(\mathbf { r } = \left( \begin{array} { l } 1
   6
   7 \end{array} \right) + \lambda \left( \begin{array} { r } 2
   - 1
   - 1 \end{array} \right) + \mu \mathbf { c }\), where \(\mathbf { c }\) is perpendicular to \(\left( \begin{array} { r } 2
   - 1
   - 1 \end{array} \right)\). Find \(\mathbf { c }\).