7 The equations of two intersecting lines are
\(\mathbf { r } = \left( \begin{array} { c } - 12
a
- 1 \end{array} \right) + \lambda \left( \begin{array} { l } 2
2
1 \end{array} \right) \quad \mathbf { r } = \left( \begin{array} { l } 2
0
5 \end{array} \right) + \mu \left( \begin{array} { c } - 3
1
- 1 \end{array} \right)\)
where \(a\) is a constant.

1. Find a vector, \(\mathbf { b }\), which is perpendicular to both lines.
2. Show that \(\mathbf { b } \cdot \left( \begin{array} { c } - 12
   a
   - 1 \end{array} \right) = \mathbf { b } \cdot \left( \begin{array} { l } 2
   0
   5 \end{array} \right)\).
3. Hence, or otherwise, find the value of \(a\).