5. Relative to a fixed origin, two lines have the equations $$\begin{aligned} & \mathbf { r } = \left( \begin{array} { l } 4
1
1 \end{array} \right) + s \left( \begin{array} { l } 1
4
5 \end{array} \right)
& \mathbf { r } = \left( \begin{array} { c } - 3
1
- 6 \end{array} \right) + t \left( \begin{array} { l } 3
a
b \end{array} \right) \end{aligned}$$ and
where \(a\) and \(b\) are constants and \(s\) and \(t\) are scalar parameters.
Given that the two lines are perpendicular,

1. find a linear relationship between \(a\) and \(b\). Given also that the two lines intersect,
2. find the values of \(a\) and \(b\),
3. find the coordinates of the point where they intersect.
   5. continued