Three identical particles with velocities `v_0hati`, `-3v_0hatj` and `5v_0hatk` collide successively with each other in such a way that they form a single particle. The velocity vector of resultant particle is

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`