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Right-hand rule

Updated: 12/20/2025, 11:17:31 AM Wikipedia source

In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field. The various right- and left-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. This can be seen by holding your hands together with palms up and fingers curled. If the curl of the fingers represents a movement from the first or x-axis to the second or y-axis, then the third or z-axis can point along either right thumb or left thumb.

Tables

For right-handed coordinates, use the right hand.For left-handed coordinates, use the left hand. · Coordinates
x (or first vector)
x (or first vector)
Axis/vector
x (or first vector)
Two fingers and thumb
First or index
Curled fingers
Fingers extended
y (or second vector)
y (or second vector)
Axis/vector
y (or second vector)
Two fingers and thumb
Second finger or palm
Curled fingers
Fingers curled 90°
z (or third vector)
z (or third vector)
Axis/vector
z (or third vector)
Two fingers and thumb
Thumb
Curled fingers
Thumb
Axis/vector
Two fingers and thumb
Curled fingers
x (or first vector)
First or index
Fingers extended
y (or second vector)
Second finger or palm
Fingers curled 90°
z (or third vector)
Thumb
Thumb

References

  1. Lectures on quaternions
    http://archive.org/details/bub_gb_TCwPAAAAIAAJ
  2. IEEE Access
    https://dx.doi.org/10.1109/access.2016.2538262
  3. Elements of Vector Analysis: Arranged for the Use of Students in Physics
    https://archive.org/details/elementsvectora00gibb
  4. Vector calculus, linear algebra, and differential forms : a unified approach
    http://archive.org/details/vectorcalculusli0000hubb
  5. Magnets and electric currents. An elementary treatise for the use of electrical artisans and science teachers
    http://archive.org/details/magnetsandelect01flemgoog
  6. udel.edu
    http://www.physics.udel.edu/~watson/phys345/Fall1998/class/1-right-hand-rule.html
  7. IIT Foundation Series: Physics – Class 8, Pearson, 2009, p. 312.
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