Lagrange's formula
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In mathematics, Lagrange's formula is a formula relating the cross product to the dot product of vectors in R3. It states,
- a × (b × c) = b(a · c) − c(a · b),
which is easier to remember as “BAC minus CAB”. This formula is very useful in simplifying vector calculations in physics. A special case regarding gradients and useful in vector calculus, is
This is a special case of the more general Laplace-de Rham operator Δ = dδ + δd.
Another useful identity of Lagrange is
This is a special case of the multiplicativity | vw | = | v | | w | of the norm in the quaternion algebra.
