In a perfectly inelastic collision the two masses will fuse and start to move together. Since there are no external forces acting on the system of particles the momentum of the system must be conserved. Let the masses be m1 and m2 and their corrosponding velocities prior to collision be v1 and v2. Let v be the final velocity of the particle. Then we have,
m1v1 + m2v2 = (m1+m2) v.
So in this problem the final velocity will be [3i -2j + 2(4j -6k) ]/(2+1) = i + 2j - 4k
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Another interesting way to look at it is to say that the centre of mass velocity doesn't change during a collision between two particles. In a perfectly inelastic collision, the particles fuse together and the resulting body co-incides with the centre of mass. Hence the centre of mass velocity before (and after) the collision is equal to the velocity of the fused body after the collision.
I am really enjoying your solutions here!
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