8 Two lines have equations
$$\mathbf { r } = \left( \begin{array} { r }
5
1
- 4
\end{array} \right) + s \left( \begin{array} { r }
1
- 1
3
\end{array} \right) \quad \text { and } \quad \mathbf { r } = \left( \begin{array} { r }
p
4
- 2
\end{array} \right) + t \left( \begin{array} { r }
2
5
- 4
\end{array} \right) ,$$
where \(p\) is a constant. It is given that the lines intersect.
- Find the value of \(p\) and determine the coordinates of the point of intersection.
- Find the equation of the plane containing the two lines, giving your answer in the form \(a x + b y + c z = d\), where \(a , b , c\) and \(d\) are integers.