(a) Two ships M and N, moving with constant velocities, have position vectors (3i + 7j) and (4i + 5j) respectively. If the velocities of M and N are (5i + 6j) and (2i + 3j) and the distance covered by the ships after t seconds are in metres, find (i) MN ; (ii) |MN|, when t = 3 seconds. (b) A particle is acted upon by forces and , where p and q are constants. If the particle remains in equilibrium under the action of these forces, find the values of p and q.
Explanation
(a)(i) Position vector of M = 3i + 7j i.e . Position vector of N = 4i + 5j i.e Velocity of M = 5i + 6j Distance covered in time t = When t = 3 seconds, = Velocity of N = 2i + 3j Distance covered in time t = When t = 3 seconds, = = = (b) If the particle remains in equilibrium, then Equating by components,
