Just like you right hand and left hands, both have 5 fingers but look different,
coordinate systems also have an orientation to them. We need to find a set of
axes. You also need to specify one other fact, whether the axes are in
right-handed or in left-handed system. Here's an example of a right-handed
coordinate system. Say, I want to build a building. I define the x-axis as going
east and the y-axis as going north. Now, my floor plan shows x pointing right, y
pointing up. This is the standard 2D Cartesian coordinate system. If I had to
find altitude as the z-axis with the arrow coming out of the diagram towards the
viewer, this is a right-handed coordinate system. Why is this right-handed?
Well, if you place your thumb along the x-axis and the index finger along the
y-axis, the middle finger is the z-axis and points towards you. You'll notice if
you try to do the same thing with your left hand, you can't match up all 3 axes,
at least not comfortably. This is a left-handed coordinate system. The key thing
to realize is that the left-handed coordinate system is equally valid. It does
not change the underlying reality of, of the situation. For example, intelligent
rabbits might agree that x is east and y is north, that's fine. However, they
might decide that the z-axis points down into the page. The rabbits care more
about how far down a tunnel is dug from ground level and want to say 5 feet,
instead of negative 5 feet when they're digging. This is a left-handed
coordinate system. The underlying reality is the same in both cases, nothing has
changed place, just how we and the rabbits refer to location differs. When we
say 12 meters, the rabbits would say, negative 12 meters and vice-versa. To
convert between these particular two systems is simply a matter of negating the
z-coordinate value.