- The line \(l _ { 1 }\) has equation \(\mathbf { r } = \left( \begin{array} { r } 2
- 3
1 \end{array} \right) + \lambda \left( \begin{array} { r } 3
4
- 1 \end{array} \right)\)
The line \(l _ { 2 }\) has equation \(\mathbf { r } = \left( \begin{array} { c } 13
5
8 \end{array} \right) + \mu \left( \begin{array} { r } 1
- 2
5 \end{array} \right)\)
where \(\lambda\) and \(\mu\) are scalar parameters.
The lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect at the point \(P\).
- Determine the coordinates of \(P\).
Given that the plane \(\Pi\) contains both \(l _ { 1 }\) and \(l _ { 2 }\)
- determine a Cartesian equation for \(\Pi\).
(ii) Determine a Cartesian equation for each of the two lines that
- pass through \(( 0,0,0 )\)
- make an angle of \(60 ^ { \circ }\) with the \(x\)-axis
- make an angle of \(45 ^ { \circ }\) with the \(y\)-axis