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bac-cab rule
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The bac-cab rule states that for vectors $\mathbf{A}$ , $\mathbf{B}$ , and $\mathbf{C}$ (that can be either real or complex) in $\sR^3$ , we have $$ \mathbf{A}\times (\mathbf{B}\times \mathbf{C}) = \mathbf{B} (\mathbf{A}\cdot \mathbf{C}) - \mathbf{C} (\mathbf{A} \cdot \mathbf{B}).$$ Here $\times$ is the cross product, and $\cdot$ is the real inner product.
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"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 5340 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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Pending Errata and Addenda
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