In this question, all distances are in metres and time, \(t\), is in seconds. A particle \(P\) moves with a speed of 14.5 parallel to the vector \(\binom{-20}{21}\). (a) Find the velocity vector of \(P\).

Initially, \(P\) has position vector \(\binom{3}{5}\). (b) Write down the position vector of \(P\) at time \(t\).

A second particle \(Q\) has position vector \(\binom{-1}{3}+\binom{-5}{7.5} t\) at time \(t\). (c) Find, in terms of \(t\), the distance between \(P\) and \(Q\) at time \(t\). Simplify your answer.

(d) Hence show that \(P\) and \(Q\) never collide.