2 Two intersecting lines, lying in a plane \(p\), have equations $$\frac { x - 1 } { 2 } = \frac { y - 3 } { 1 } = \frac { z - 4 } { - 3 } \quad \text { and } \quad \frac { x - 1 } { - 1 } = \frac { y - 3 } { 2 } = \frac { z - 4 } { 4 } .$$

1. Obtain the equation of \(p\) in the form \(2 x - y + z = 3\).
2. Plane \(q\) has equation \(2 x - y + z = 21\). Find the distance between \(p\) and \(q\).