A command post (O) monitors th movement of two ships in the gulf. At 1200 hrs a battleship (b) has bosition (-2i+10j)km relative to (O) and has constant velocity of (3i+2j)km/h , where I and j are unit vectors directed due east and due north respectively .

a)the captain of one ship has e been taken ill , show that the two ships will collide . The command post contacts the battleship and orders it to reduce its speed to move with velocity (2i+2j)km/h

b)find an expression for the vector [BF] at time t hours after noon

c)find the distance between B and F at 1400hrs

d)find the time at which F will be due north of B