# generalization of the parallelogram law

###### Theorem.

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

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

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

Title generalization of the parallelogram law GeneralizationOfTheParallelogramLaw 2013-03-22 16:08:53 2013-03-22 16:08:53 Mathprof (13753) Mathprof (13753) 10 Mathprof (13753) Theorem msc 46C05 ParallelogramLaw2