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Mathematics-Online lexicon:

Vector Product

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The vector

$\displaystyle \vec{c} = \vec{a} \times \vec{b} $

is orthogonal to $ \vec{a}$ and $ \vec{b}$. It is oriented by the ,,Right-Hand-Rule`` and has the length

$\displaystyle \bigl\vert\vec{c}\bigr\vert = \bigl\vert\vec{a}\bigr\vert\bigl\vert\vec{b}\bigr\vert\sin(\sphericalangle(\vec{a},\vec{b}))\, . $

\includegraphics[width=0.6\linewidth]{vektorprodukt_en.eps}

Alternatively, we have

\begin{displaymath} \vec{a}\times\vec{b}=\left( \begin{array}{c} a_2 b_3 - a_... ..._3 b_1 - a_1 b_3 \\ a_1 b_2 - a_2 b_1 \end{array} \right) \end{displaymath}

Examples:

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  automatically generated 3/17/2011