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Mathematics-Online lexicon:

Vector Product


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

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