Right-hand Rule - Right-handed and Left-handed Co-ordinates

Right-handed and Left-handed Co-ordinates

Let the X and Y axes define a horizontal plane with the X-axis pointing toward you. Then the Z-axis can either point up (right-handed) or down (left-handed). If the co-ordinates are right-handed and you place your right fist on the plane then your fingers will curl from the first or X-axis to the second or Y-axis and your thumb will point along the Z-axis. If the co-ordinates were left handed the fingers of your left hand would curl from the first axis to the second and your left thumb would point along the Z-axis.

If any one axis is reversed the handedness changes. To preserve handedness one of the other axes must also reverse which is equivalent to switching the labels on the other two axes. Note that the handedness of co-ordinates has no meaning unless the axes are labled in sequence: 1,2,3 or x,y,z.