1 Determine whether the lines $$\frac { x - 1 } { 1 } = \frac { y + 2 } { - 1 } = \frac { z + 4 } { 2 } \quad \text { and } \quad \frac { x + 3 } { 2 } = \frac { y - 1 } { 3 } = \frac { z - 5 } { 4 }$$ intersect or are skew.
\(2 \quad H\) denotes the set of numbers of the form \(a + b \sqrt { 5 }\), where \(a\) and \(b\) are rational. The numbers are combined under multiplication.

1. Show that the product of any two members of \(H\) is a member of \(H\). It is now given that, for \(a\) and \(b\) not both zero, \(H\) forms a group under multiplication.
2. State the identity element of the group.
3. Find the inverse of \(a + b \sqrt { 5 }\).
4. With reference to your answer to part (iii), state a property of the number 5 which ensures that every number in the group has an inverse.