1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors due east and due north respectively. Position vectors are given relative to a fixed origin \(O\).]

Two ships \(P\) and \(Q\) are moving with constant velocities. Ship \(P\) moves with velocity \(( 2 \mathbf { i } - 3 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\) and ship \(Q\) moves with velocity \(( 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\).

1. Find, to the nearest degree, the bearing on which \(Q\) is moving. At 2 pm , ship \(P\) is at the point with position vector \(( \mathbf { i } + \mathbf { j } ) \mathrm { km }\) and \(\operatorname { ship } Q\) is at the point with position vector \(( - 2 \mathbf { j } ) \mathrm { km }\). At time \(t\) hours after 2 pm , the position vector of \(P\) is \(\mathbf { p } \mathrm { km }\) and the position vector of \(Q\) is \(\mathbf { q } \mathrm { km }\).
2. Write down expressions, in terms of \(t\), for
   1. \(\mathbf { p }\),
   2. \(\mathbf { q }\),
   3. \(\overrightarrow { P Q }\).
3. Find the time when
   1. \(Q\) is due north of \(P\),
   2. \(Q\) is north-west of \(P\).