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