Mathematics-Online course: Preparatory Course Mathematics-Linear Algebra and Geometry-Vectors-Cross Product

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	Mathematics-Online course: Preparatory Course Mathematics - Linear Algebra and Geometry - Vectors
	Cross 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

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

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automatically generated 1/9/2017