Cartesian Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 16

Figure 1.12
Left-handed coordinate space
Now perform the same experiment with your right hand. Notice that
your index finger still points up, and your third finger points forward. How-
ever, with your right hand, your thumb will point to the left. This is
a right-handed coordinate system. Again, your thumb, index finger, and
third finger point in the +x, +y, and +z directions, respectively. A right-
handed coordinate system is shown in Figure 1.13.
Figure 1.13
Right-handed coordinate space
Try as you might, you cannot rotate your hands into a position such
that all three fingers simultaneously point the same direction on both hands.
(Bending your fingers is not allowed.)
Left-handed and right-handed coordinate systems also differ in the defi-
nition of “positive rotation.” Let's say we a have line in space and we need
to rotate about this line by a specified angle. We call this line an axis of
rotation, but don't think that the word axis implies that we're talking only
about one of the cardinal axes (the x-, y-, or z-axis). An axis of rotation
can be arbitrarily oriented. Now, if you tell me to “rotate 30 o about the