If you do it the other way around, you'll get the same answers (as long as you are consistent).
I actually sometimes do it the other way around (because when I visualize 3D coords, the Z axis goes out forward in front of me, so pointing my thumb in the positive direction makes my fingers curl clockwise)
So for my X and Y axes it's "the right hand rule" but for my Z axis, (in order to be consistent,) it's "the left hand rule"
(I could just flip my Z axis, but that's very unnatural to me, especially when the Z axis represents time)Like Ultrafast said, it's just a convention.I just wanted to point out that "the right hand rule" only works if you follow another arbitrary convention (the conventional positive/negative directions of each axis)