Question
Two particles A and B, move with constant velocities v1 and v2. At the initial moment, their position vectors are r1 and r2 respectively. The condition for particles A and B for their collision is
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r1.v1 = r2.v2
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r1 x v1 = r2 x v2
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r1 - r2 = v1-v2
Solution
A.
For two particles A and B moves with constant velocitites v1 and v2, such that two particles to collide, the direction of the relative velocity of one with respect to other should be directed towards the relative position of the other particle.i.e., 
direction of relative position of 1 w.r.t
similarly, 
direction of velocity of 2 w.r.t 1
so, for collision of A and B, we get
