(CIE 0606/2021/m/12/Q5) In this question all lengths are in kilometres and time is in hours. Boat A sails, with constant velocity, from a point $O$ with position vector $\cvec{0}{0}$. After 3 hours $A$ is at the
point with position vector $\cvec{-12}{9.}$
(a) Find the position vector, $\ABvec{OP},$ of $A$ at time $t$. [1]
At the same time as $A$ sails from $O$, boat $B$ sails from a point with position vector $\cvec{12}{6},$ with constant velocity $\cvec{-5}{8}$.
(b) Find the position vector, $\ABvec{OQ},$ of $B$ at time $t.$ [1]
(c) Show that at time $t, |\ABvec{PQ}|^2=26t^2+36t+180.$ [3]
(d) Hence show that $A$ and $B$ do not collide. [2]
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