6 Lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations
$$\frac { x - 3 } { 2 } = \frac { y - 4 } { - 1 } = \frac { z + 1 } { 1 } \quad \text { and } \quad \frac { x - 5 } { 4 } = \frac { y - 1 } { 3 } = \frac { z - 1 } { 2 }$$
respectively.
- Find the equation of the plane \(\Pi _ { 1 }\) which contains \(l _ { 1 }\) and is parallel to \(l _ { 2 }\), giving your answer in the form r.n \(= p\).
- Find the equation of the plane \(\Pi _ { 2 }\) which contains \(l _ { 2 }\) and is parallel to \(l _ { 1 }\), giving your answer in the form r.n \(= p\).
- Find the distance between the planes \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\).
- State the relationship between the answer to part (iii) and the lines \(l _ { 1 }\) and \(l _ { 2 }\).