parallelogram lawParallelogramLaw22006-08-02 22:55:012006-10-04 19:11:10Theorem% this is the default PlanetMath preamble. as your knowledge
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\usepackage{amssymb}
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\newtheorem{thm}{Theorem}
\begin{thm} In an \PMlinkname{inner product space}{InnerProductSpace}, let $x$ and $y$ be vectors. Then
$$ \Vert x + y \Vert ^ 2 + \Vert x - y \Vert ^2 = 2 \Vert x \Vert ^ 2 + 2 \Vert y \Vert ^ 2.$$
\end{thm}