8 The points \(A , B\) and \(C\) have coordinates \(( 2 , - 1 , - 5 ) , ( 0,5 , - 9 )\) and \(( 9,2,3 )\) respectively.
The line \(l\) has equation \(\mathbf { r } = \left[ \begin{array} { r } 2
- 1
- 5 \end{array} \right] + \lambda \left[ \begin{array} { r } 1
- 3
2 \end{array} \right]\).
- Verify that the point \(B\) lies on the line \(l\).
- Find the vector \(\overrightarrow { B C }\).
- The point \(D\) is such that \(\overrightarrow { A D } = 2 \overrightarrow { B C }\).
- Show that \(D\) has coordinates \(( 20 , - 7,19 )\).
- The point \(P\) lies on \(l\) where \(\lambda = p\). The line \(P D\) is perpendicular to \(l\). Find the value of \(p\).