4 The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed due east and due north respectively.
Two cyclists, Aazar and Ben, are cycling on straight horizontal roads with constant velocities of \(( 6 \mathbf { i } + 12 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\) and \(( 12 \mathbf { i } - 8 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\) respectively. Initially, Aazar and Ben have position vectors \(( 5 \mathbf { i } - \mathbf { j } ) \mathrm { km }\) and \(( 18 \mathbf { i } + 5 \mathbf { j } ) \mathrm { km }\) respectively, relative to a fixed origin.

1. Find, as a vector in terms of \(\mathbf { i }\) and \(\mathbf { j }\), the velocity of Ben relative to Aazar.
2. The position vector of Ben relative to Aazar at time \(t\) hours after they start is \(\mathbf { r } \mathrm { km }\). Show that $$\mathbf { r } = ( 13 + 6 t ) \mathbf { i } + ( 6 - 20 t ) \mathbf { j }$$
3. Find the value of \(t\) when Aazar and Ben are closest together.
4. Find the closest distance between Aazar and Ben.