# generalization of the parallelogram law

###### Theorem.

In an inner product space^{} (http://planetmath.org/InnerProductSpace), let $x\mathrm{,}y\mathrm{,}z$ be vectors. Then

$${\parallel x+y\parallel}^{2}+{\parallel y+z\parallel}^{2}+{\parallel z+x\parallel}^{2}={\parallel x\parallel}^{2}+{\parallel y\parallel}^{2}+{\parallel z\parallel}^{2}+{\parallel x+y+z\parallel}^{2}.$$ |

Taking $x+z=0$ we have the usual parallelogram law^{}.

Title | generalization^{} of the parallelogram law |
---|---|

Canonical name | GeneralizationOfTheParallelogramLaw |

Date of creation | 2013-03-22 16:08:53 |

Last modified on | 2013-03-22 16:08:53 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 10 |

Author | Mathprof (13753) |

Entry type | Theorem |

Classification | msc 46C05 |

Related topic | ParallelogramLaw2 |