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Mathematics-Online lexicon:

Triangle Inequality

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

For the sum of two vectors the following holds:

$\displaystyle \vert\vec{a}+\vec{b}\vert \le \vert\vec{a}\vert + \vert\vec{b}\vert\,.

We have equality if and only if $ \vec{a}$ and $ \vec{b}$ are parallel, that is $ \vec{a}=s\vec{b}$ with $ s \geq 0$ .


  automatically generated 3/28/2008