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

Two cars \(P\) and \(Q\) are moving on straight horizontal roads with constant velocities. The velocity of \(P\) is \(( 15 \mathbf { i } + 20 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and the velocity of \(Q\) is \(( 20 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)

1. Find the direction of motion of \(Q\), giving your answer as a bearing to the nearest degree. At time \(t = 0\), the position vector of \(P\) is \(400 \mathbf { i }\) metres and the position vector of \(Q\) is 800j metres. At time \(t\) seconds, the position vectors of \(P\) and \(Q\) are \(\mathbf { p }\) metres and \(\mathbf { q }\) metres respectively.
2. Find an expression for
   1. \(\mathbf { p }\) in terms of \(t\),
   2. \(\mathbf { q }\) in terms of \(t\).
3. Find the position vector of \(Q\) when \(Q\) is due west of \(P\).