7. Relative to a fixed origin, the points \(A\) and \(B\) have position vectors \(\left( \begin{array} { c } - 4
1
3 \end{array} \right)\) and \(\left( \begin{array} { c } - 3
6
1 \end{array} \right)\) respectively.
- Find a vector equation for the line \(l _ { 1 }\) which passes through \(A\) and \(B\).
The line \(l _ { 2 }\) has vector equation
$$\mathbf { r } = \left( \begin{array} { c }
3
- 7
9
\end{array} \right) + t \left( \begin{array} { c }
2
- 3
1
\end{array} \right)$$ - Show that lines \(l _ { 1 }\) and \(l _ { 2 }\) do not intersect.
- Find the position vector of the point \(C\) on \(l _ { 2 }\) such that \(\angle A B C = 90 ^ { \circ }\).