2 The equations of two intersecting lines \(l _ { 1 }\) and \(l _ { 2 }\) are
\(l _ { 1 } : \mathbf { r } = \left( \begin{array} { l } 1
0
a \end{array} \right) + \lambda \left( \begin{array} { r } 2
1
- 3 \end{array} \right) \quad l _ { 2 } : \mathbf { r } = \left( \begin{array} { r } 7
9
- 2 \end{array} \right) + \mu \left( \begin{array} { r } - 1
1
2 \end{array} \right)\)
where \(a\) is a constant.
The equation of the plane \(\Pi\) is
r. \(\left( \begin{array} { l } 1
5
3 \end{array} \right) = - 14\).
\(l _ { 1 }\) and \(\Pi\) intersect at \(Q\).
\(\zeta _ { 2 }\) and \(\Pi\) intersect at \(R\).

1. Verify that the coordinates of \(R\) are \(( 13,3 , - 14 )\).
2. Determine the exact value of the length of \(Q R\).