7 The points \(A\) and \(B\) have coordinates ( \(3 , - 2,5\) ) and ( \(4,0,1\) ) respectively. The line \(l _ { 1 }\) has equation \(\mathbf { r } = \left[ \begin{array} { r } 6
- 1
5 \end{array} \right] + \lambda \left[ \begin{array} { r } 2
- 1
4 \end{array} \right]\).

1. Find the distance between the points \(A\) and \(B\).
2. Verify that \(B\) lies on \(l _ { 1 }\).
   (2 marks)
3. The line \(l _ { 2 }\) passes through \(A\) and has equation \(\mathbf { r } = \left[ \begin{array} { r } 3
   - 2
   5 \end{array} \right] + \mu \left[ \begin{array} { r } - 1
   3
   - 8 \end{array} \right]\). The lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect at the point \(C\). Show that the points \(A , B\) and \(C\) form an isosceles triangle.
   (6 marks)