6 The line \(l\) has equations \(\frac { x - 1 } { 2 } = \frac { y + 2 } { 3 } = \frac { z - 7 } { 5 }\). The plane \(\Pi\) has equation \(4 x - y - z = 8\).
- Show that \(l\) is parallel to \(\Pi\) but does not lie in \(\Pi\).
- The point \(A ( 1 , - 2,7 )\) is on \(l\). Write down a vector equation of the line through \(A\) which is perpendicular to \(\Pi\). Hence find the position vector of the point on \(\Pi\) which is closest to \(A\).
- Hence write down a vector equation of the line in \(\Pi\) which is parallel to \(l\) and closest to it.