Mathematics-Online lexicon: Parametric Representation of a Plane

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	Mathematics-Online lexicon:
	Parametric Representation of a Plane

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

The points in a plane through

spanned by two nonparallel directions $\vec{u}$ und $\vec{v}$ satisfy

$\displaystyle \overrightarrow{PX} = s\vec{u}+t\vec{v},\quad s,t\in\mathbb{R}\, .$

$\includegraphics[width=10cm]{param_darst}$

Correspondingly, we have

$\displaystyle x_i = p_i + su_i+tv_i,\quad i=1,2,3\, .$

for the coordinates of the position vector $\vec{x}$ .

Example:

automatically generated 3/28/2008