6. A small boat \(S\), drifting in the sea, is modelled as a particle moving in a straight line at constant speed. When first sighted at \(0900 , S\) is at a point with position vector \(( 4 \mathbf { i } - 6 \mathbf { j } ) \mathrm { km }\) relative to a fixed origin \(O\), where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors due east and due north respectively. At \(0945 , S\) is at the point with position vector ( \(7 \mathbf { i } - 7.5 \mathbf { j }\) ) km. At time \(t\) hours after 0900, \(S\) is at the point with position vector \(\mathbf { s } \mathrm { km }\).

1. Calculate the bearing on which \(S\) is drifting.
2. Find an expression for \(\mathbf { s }\) in terms of \(t\). At 1000 a motor boat \(M\) leaves \(O\) and travels with constant velocity ( \(p \mathbf { i } + q \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\). Given that \(M\) intercepts \(S\) at 1015,
3. calculate the value of \(p\) and the value of \(q\).
   (6)