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right-hand rule
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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. right-hand rule for vector cross product
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right-hand rule

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A.
vector mathematics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

The right-hand rule is a mnemonic device used in physics and mathematics to determine the direction of vectors resulting from certain operations. It's particularly useful when dealing with vectors, which are quantities possessing both magnitude and direction.1

One key application is in the cross product of two vectors. If you point the thumb of your right hand in the direction of the first vector and curl your fingers towards the second vector, your thumb will indicate the direction of the resulting cross product vector. This resulting vector is perpendicular to both of the original vectors. The rule also helps determine the direction of induced electromotive force in electricity when a conductor moves relative to a magnetic field.23

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  1. right-hand rule
  2. cross product
  3. vector

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