Right-hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding the orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of the cross-product of 2 vectors. Rather than a mathematical fact, it is a convention, closely related to the convention that rotation around a vertical axis is positive if it is counterclockwise, and negative if it is clockwise.

Finding the direction of the cross product by the right-hand rule

Most of the various left-hand and right-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations.[1] One can see this by holding one's hands outward and together, palms up, with the thumbs out-stretched to the right and left, and the fingers making a curling motion from straight outward to pointing upward. (Note the hand picture is not an illustration of this.) If the curling motion of the fingers represents a movement from the first (x-axis) to the second (y-axis), then the third (z-axis) can point along either thumb. Left-hand and right-hand rules arise when dealing with coordinate axes. The rule can be used to find the direction of the magnetic field, rotation, spirals, electromagnetic fields, mirror images, and enantiomers in mathematics and chemistry.

The sequence is often: index finger, middle finger, thumb. Two other sequences also work because they preserve the cycle:

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