6. With respect to a fixed origin \(O\), the lines \(l _ { 1 }\) and \(l _ { 2 }\) are given by the equations
$$l _ { 1 } : \mathbf { r } = \left( \begin{array} { r }
4
28
4
\end{array} \right) + \lambda \left( \begin{array} { r }
- 1
- 5
1
\end{array} \right) , \quad l _ { 2 } : \mathbf { r } = \left( \begin{array} { l }
5
3
1
\end{array} \right) + \mu \left( \begin{array} { r }
3
0
- 4
\end{array} \right)$$
where \(\lambda\) and \(\mu\) are scalar parameters.
The lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect at the point \(X\).
- Find the coordinates of the point \(X\).
- Find the size of the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\), giving your answer in degrees to 2 decimal places.
The point \(A\) lies on \(l _ { 1 }\) and has position vector \(\left( \begin{array} { r } 2
18
6 \end{array} \right)\) - Find the distance \(A X\), giving your answer as a surd in its simplest form.
The point \(Y\) lies on \(l _ { 2 }\). Given that the vector \(\overrightarrow { Y A }\) is perpendicular to the line \(l _ { 1 }\)
- find the distance \(Y A\), giving your answer to one decimal place.
The point \(B\) lies on \(l _ { 1 }\) where \(| \overrightarrow { A X } | = 2 | \overrightarrow { A B } |\).
- Find the two possible position vectors of \(B\).