A flight controller at an airport observes two aircrafts A & B simultaneously, their position vector being respectively (10i + 20j + 5k)km and (-20i – 10j + 3k)km relative to the control tower. A, flying with a constant velocity of (-40i – 50j)km/h and B, with a constant velocity of (150i + 250j + 60k)km/h.

Find

(i) the velocity of A relative to B

(ii) the position of A relative to B, t minutes after the aircrafts are observed.

(iii) the value of t, correct to the nearest 10s, when A and B are nearest to each other.