8. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors directed due east and due north respectively and position vectors are given relative to a fixed origin.] A ship \(A\) moves with constant velocity \(( 3 \mathbf { i } - 10 \mathbf { j } ) \mathrm { kmh } ^ { - 1 }\)
At time \(t\) hours, the position vector of \(A\) is \(\mathbf { r } \mathrm { km }\).
At time \(t = 0 , A\) is at the point with position vector \(( 13 \mathbf { i } + 5 \mathbf { j } ) \mathrm { km }\).

1. Find \(\mathbf { r }\) in terms of \(t\). Another ship \(B\) moves with constant velocity \(( 15 \mathbf { i } + 14 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\)
   At time \(t = 0 , B\) is at the point with position vector \(( 3 \mathbf { i } - 5 \mathbf { j } ) \mathrm { km }\).
2. Show that, at time \(t\) hours, $$\overrightarrow { A B } = [ ( 12 t - 10 ) \mathbf { i } + ( 24 t - 10 ) \mathbf { j } ] \mathrm { km }$$ Given that the two ships do not change course,
3. find the shortest distance between the two ships,
4. find the bearing of ship \(B\) from ship \(A\) when the ships are closest.
   
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