In free space, three identical particles moving with velocities `v_(0)hat(i), - 3v_(0)hat(j)` and `5v_(0)hat(k)` collide successively with each other to form a single particle. Find velocity vector of the particle formed.

Explanation

Let m be the mass of a single particle before any of the collisions. The mas of particles formed after collidions must be 3m. In free space, no external forces act on any of the particles, their total momentum remains conserved.
Applying principle of conservation of momentum, we have
`sum vec(p)_("initial") = sum vec(p)_("final") rarr mv_(0)hat(i)- 3mv_(0)hat(j) + 5mv_(0)hat(k) = 3m vec(v)`
`vec(v)= 1/3v_(0)(hat(i) - 3hat(j) + 5hat(k))m//s`