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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 overview

The points in a plane through $ P$ 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:


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  automatically generated 3/28/2008