Answer 2—A right-handed coordinate system is a set of three axes (x, y, z) that have the relationship that if you orient the curled fingers of your right hand so that they point from the positive x-axis to the positive y-axis, the thumb of that hand points in the direction of the positive z-axis. You can create a different coordinate system, with the z-axis pointing the other way, using your left hand.

All other combinations of x-, y-, and z-axes can be rotated to match one of these two basic systems, which makes this the only important distinction that needs to be made.