Can u explain relative velocity in datail?

its an interesting topic regarding kinematics............first see weather the motion of particles are in same direction or opposite direction for same direction it is let v` is the relative velocity of particle A w.r.t. B for particle A velocity w.r.t. earth is v``& velocity of B w.r.t. earth is v```............now v`=v``-v``` for opposite direction take - sign  example v`=v``+v```