- The plane \(\Pi\) has equation
$$3 x + 4 y - z = 17$$
The line \(l _ { 1 }\) is perpendicular to \(\Pi\) and passes through the point \(P ( - 4 , - 5,3 )\)
The line \(l _ { 1 }\) intersects \(\Pi\) at the point \(Q\)
- Determine the coordinates of \(Q\)
Given that the point \(R ( - 1,6,4 )\) lies on \(\Pi\)
- determine a Cartesian equation of the plane containing \(P Q R\)
The line \(l _ { 2 }\) passes through \(P\) and \(R\)
The line \(l _ { 3 }\) is the reflection of \(l _ { 2 }\) in \(\Pi\) - Determine a vector equation for \(l _ { 3 }\)