Right hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation conventions for vectors in three dimensions.

Most of the various left and right-hand rules arise from the fact that the three axes of 3-dimensional space have two possible orientations. This can be seen by holding your hands outward and together, palms up, with the fingers curled. If the curl of your fingers represents a movement from the first or X axis to the second or Y axis then the third or Z axis can point either along your left thumb or right thumb. Left and right-hand rules arise when dealing with co-ordinate axes, rotation, spirals, electromagnetic fields, mirror images and enantiomers in mathematics and chemistry.

Coordinates are usually right-handed.

For right-handed coordinates your right thumb points along the Z axis in a positive Z-direction and the curl of your fingers represents a motion from the first or X axis to the second or Y axis. When viewed from the top or Z axis the system is counter-clockwise.

For left-handed coordinates your left thumb points along the Z axis in a positive Z-direction and the curled fingers of your left hand represent a motion from the first or X axis to the second or Y axis. When viewed from the top or Z axis the system is clockwise.

Interchanging the labels of any two axes reverses the handedness. Reversing the direction of one axis (or of all three axes) also reverses the handedness. (If the axes do not have a positive or negative direction then handedness has no meaning.) Reversing two axes amounts to a 180° rotation around the remaining axis.

In mathematics a rotating body is commonly represented by a vector along the axis of rotation. The length of the vector gives the speed of rotation and the direction of the axis gives the direction of rotation according to the right-hand rule: right fingers curled in the direction of rotation and the right thumb pointing in the positive direction of the axis. This allows some easy calculations using the vector cross product. Note that no part of the body is moving in the direction of the axis arrow, which takes some getting used to. By coincidence, if your thumb points north the earth rotates according to the right-hand rule. This causes the sun and stars to appear to revolve according to the left-hand rule.

A helix, to use a more accurate term than spiral, is basically a circular curve that advances along the z-axis while rotating in the x-y plane. Helices are either right- or left-handed, curled fingers giving the direction of rotation and thumb giving the direction of advance. The two types are mirror images of each other, physically distinct and cannot be transformed into each other by any physical operation such as turning them over.

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