4. Two ships \(P\) and \(Q\) are moving along straight lines with constant velocities. Initially \(P\) is at a point \(O\) and the position vector of \(Q\) relative to \(O\) is ( \(6 \mathbf { i } + 12 \mathbf { j }\) ) km , where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors directed due east and due north respectively. The ship \(P\) is moving with velocity \(10 \mathbf { j } \mathrm {~km} \mathrm {~h} ^ { - 1 }\) and \(Q\) is moving with velocity \(( - 8 \mathbf { i } + 6 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\). At time \(t\) hours the position vectors of \(P\) and \(Q\) relative to \(O\) are \(\mathbf { p } \mathrm { km }\) and \(\mathbf { q } \mathrm { km }\) respectively.

1. Find \(\mathbf { p }\) and \(\mathbf { q }\) in terms of \(t\).
2. Calculate the distance of \(Q\) from \(P\) when \(t = 3\).
3. Calculate the value of \(t\) when \(Q\) is due north of \(P\).