How do I use this confusing elastic collision equation?

[SecretSnow]

Hi guys, this is the equation of relative velocities in elastic collisions:
Va1x-Vb1x = -(Va2x-Vb2x)
I know that this means that the relative velocity of A to B before an elastic collision is the same in magnitude but opposite in direction after the collision. However, this applies only in the x direction (for this particular equation). My questions are:

1. Can it be applied to y and z directions?

2. If so, then if initially A and B are of different velocity in 2D (x and y directions only) and I compare their relative velocities of x and y before and after, does the equation applies?

3. If initially A is only moving in the x direction and B is at rest, and after the elastic collision A and B are scattered in an x-y plane, does the equation for relative velocity of y still apply? Note that initially A does not have any y velocity so if I apply the equation, they should have equal y velocities magnitude. Yet if they don't have the same mass, then the conservation of momentum in the y direction is broken since there's a net y momentum from 0 y momentum initially (note that the question doesn't have external forces at all) does this mean that it is not possible to use this equation in y and z direction? So that a system without initial net y velocity or momentum cannot use the equation given above even if its an elastic collision??

Thanks a lot guys!

 

[mfb]

That equation works for one-dimensinal collisions only.
In two (or more) dimensions, you can get similar equations using momentum and energy conservation.

 

[SecretSnow]

That equation works for one-dimensinal collisions only.
In two (or more) dimensions, you can get similar equations using momentum and energy conservation.

Oh you i just realized that. That equation don't work for anything more than 1D. Thanks!