How would the relativistic velocities interact with one another in 3 dimensions?
I’m not sure what you mean by “interact”. The relativistic addition of velocities is needed when is not small; the formulae are valid whether or not and components are relativistic. If is not along the x-axis, one can generalize the addition formulae, although typically what one does is to rotate the coordinate system so that the direction is along the direction of motion, do the transforms, and then rotate back (although typically we will not be doing such problems in this course).
