Question

a molecule collides with another stationary molecule of the same mass . assume that the collision is elastic and velocities after collision V1 & V2. show that V1.V2 = 0

Answer 1

Your question is answered on the Wikipedia page for elastic collisions: http://en.wikipedia.org/wiki/Elastic_collision
It is under the section labeled "One-dimensional Newtonian"

Answer 2

what it proves is that the difference between the initial and final velocities will be equal and opposite (in other words, they will 'replace' each other in terms of relative velocity). In our case, since the 2nd one had an initial velocity of zero, the 1st one will replace it in that regard, leaving v1*v2=0 true before and after the collision.

Answer 3

what it proves is that the difference between the initial and final velocities will be equal and opposite (in other words, they will 'replace' each other in terms of relative velocity). In our case, since the 2nd one had an initial velocity of zero, the 1st one will replace it in that regard, leaving v1*v2=0 true before and after the collision.