8. Relative to a fixed origin \(O\), the lines \(l _ { 1 }\) and \(l _ { 2 }\) are given by the equations
$$\begin{aligned}
& l _ { 1 } : \quad \mathbf { r } = \left( \begin{array} { r }
4
- 3
2
\end{array} \right) + \lambda \left( \begin{array} { r }
3
- 2
- 1
\end{array} \right) \quad \text { where } \lambda \text { is a scalar parameter }
& l _ { 2 } : \quad \mathbf { r } = \left( \begin{array} { r }
2
0
- 9
\end{array} \right) + \mu \left( \begin{array} { r }
2
- 1
- 3
\end{array} \right) \quad \text { where } \mu \text { is a scalar parameter }
\end{aligned}$$
Given that \(l _ { 1 }\) and \(l _ { 2 }\) meet at the point \(X\),
- find the position vector of \(X\).
The point \(P ( 10 , - 7,0 )\) lies on \(l _ { 1 }\)
The point \(Q\) lies on \(l _ { 2 }\)
Given that \(\overrightarrow { P Q }\) is perpendicular to \(l _ { 2 }\) - calculate the coordinates of \(Q\).