This distinction arises from the fact that once two perpendicular directions have been chosen for the x and y axes, there are two possible choices for the positive side of z.
The coordinate system i, j, k is called right handed, if the three vectors are situated like the thumb, index finger and middle finger (pointing straight up from your palm) of your right hand. Alternatively, imagine you are gripping the z axis in a fist in such a way that your fingers curl round from x to y; the direction your thumb points in gives the positive zaxis of the righthanded system for the right hand; and likewise for left.
Another way of determining handedness of axes is as follows:
Lefthanded on the left, righthanded on the right.
See also chirality.
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