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Mathematics-Online course: Vector Calculus - Planes

Parametric Equation of a Plane

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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}$ .

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  automatically generated 10/30/2007