- The line \(l _ { 1 }\) has equation \(\mathbf { r } = \left( \begin{array} { r } - 2
2
0 \end{array} \right) + \lambda \left( \begin{array} { l } 3
0
1 \end{array} \right)\) where \(\lambda\) is a scalar parameter.
The line \(l _ { 2 }\) is parallel to \(\left( \begin{array} { r } 1
2
- 3 \end{array} \right)\)
- Show that \(l _ { 1 }\) and \(l _ { 2 }\) are perpendicular.
The plane \(\Pi\) contains the line \(l _ { 1 }\) and is perpendicular to \(\left( \begin{array} { r } 1
2
- 3 \end{array} \right)\) - Determine a Cartesian equation of \(\Pi\)
- Verify that the point \(A ( 3,1,1 )\) lies on \(\Pi\)
Given that
- the point of intersection of \(\Pi\) and \(l _ { 2 }\) has coordinates \(( 2,3,2 )\)
- the point \(B ( p , q , r )\) lies on \(l _ { 2 }\)
- the distance \(A B\) is \(2 \sqrt { 5 }\)
- \(p , q\) and \(r\) are positive integers
- determine the coordinates of \(B\).