# bac-cab rule

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

$$\mathbf{A}\times (\mathbf{B}\times \mathbf{C})=\mathbf{B}(\mathbf{A}\cdot \mathbf{C})-\mathbf{C}(\mathbf{A}\cdot \mathbf{B}).$$ |

Here $\times $ is the cross product^{}, and $\cdot $ is the real inner product.

Title | bac-cab rule |
---|---|

Canonical name | BaccabRule |

Date of creation | 2013-03-22 14:04:34 |

Last modified on | 2013-03-22 14:04:34 |

Owner | williamschips (4069) |

Last modified by | williamschips (4069) |

Numerical id | 6 |

Author | williamschips (4069) |

Entry type | Result |

Classification | msc 15A72 |

Classification | msc 15A90 |