Right-hand rule

In mathematics and physics, the right-hand rule is a mnemonic for understanding the orientation of axes in three-dimensional space. It is a convenient method for determining the direction of the cross product of two vectors. Rather than a mathematical fact, it is a convention. The right-hand rule is closely related to the convention that rotation is represented by a vector oriented such that if one were to view the rotation from the direction towards which the vector points, the rotation appears counter-clockwise.

Left-hand and right-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations.[1] This can be seen 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. 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. 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 along the first vector, then middle finger along the second, then thumb along the third. Two other sequences also work because they preserve the cyclic nature of the cross product (and the underlying Levi-Civita symbol):

• Middle finger, thumb, index finger.
• Thumb, index finger, middle finger.