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[parent] bac-cab rule (Result)

The bac-cab rule states that for vectors $ \mathbf{A}$, $ \mathbf{B}$, and $ \mathbf{C}$ (that can be either real or complex) in $ \mathbb{R}^3$, we have

$\displaystyle \mathbf{A}\times (\mathbf{B}\times \mathbf{C}) = \mathbf{B} (\mathbf{A}\cdot \mathbf{C}) - \mathbf{C} (\mathbf{A} \cdot \mathbf{B}).$
Here $ \times$ is the cross product, and $ \cdot$ is the real inner product.



"bac-cab rule" is owned by williamschips. [ owner history (1) ]
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Cross-references: inner product, cross product, complex, real, vectors

This is version 3 of bac-cab rule, born on 2003-11-27, modified 2003-12-01.
Object id is 5436, canonical name is BacCabRule.
Accessed 4147 times total.

Classification:
AMS MSC: 15A72 (Linear and multilinear algebra; matrix theory :: Vector and tensor algebra, theory of invariants)
 15A90 (Linear and multilinear algebra; matrix theory :: Applications of matrix theory to physics)
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