At t=0, two particles have position vectors (in metres) rA0=2i^+3j^ and rB0=8i^−5j^. Their constant velocity vectors are vA=4i^+0j^ and vB=−2i^+6j^ respectively.
(i) Write the position vectors of particles A and B as functions of time t.
(ii) Hence obtain the position vector of A relative to B and the square of their separation as functions of time.
(iii) Find the time at which the two particles are closest to each other.
(iv) Determine this minimum separation.