A 0.500 kg sphere moving with a velocity (2.00 - 2.60 + 1.00) m/s strikes another sphere of mass 1.50 kg moving with a velocity (-1.00 + 2.00 - 3.00) m/s. (a) If the velocity of the 0.500 kg sphere after the collision is (-1.00 + 3.00 - 8.00) m/s, find the velocity of the 1.50 kg sphere and identify the kind of collision (elastic ,in etc) (b) If the velocity of the 0.500 kg sphere after the collision is (-0.250 + 0.850 - 2.00) m/s, find the final velocity of the 1.50 kg sphere and identify the kind of collision.
Please explain with steps :)

Steps: first think about conservation of momentum. You have enough data to calculate the momentum of the system prior to the collision, which you know is equal to the momentum of the system after the collision. From that you can find the velocity of the 1.5 Kg mass after the collision. And from that, you can find the change in total KE of the system (if any). What do you get?

But the actual problem is solving problem in this form like in I j and k please tell me on how to solve with them

Since momentum is a vector you perform momentum calculations maintaining the i, j and k coordinates. Hence system momentum in the i direction is 0.5 Kg x 2 m/s + 1.5 Kg x -1 m/s. Kinetic energy on the other hand is a scalar, and its magnitude is (1/2)m v^2 where v is the total velocity. Hence the initial KE of mass 1 is (1/2)(0.5 Kg) [( 2 m/s)^2 + (-2.6 m.s)^2 + (1 m/s)^2].