Mathematics-Online lexicon: Distance Point

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	Mathematics-Online lexicon:
	Distance Point - Line

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 projection

of a point

on a line through

with direction $\vec{u}$ satisfies

$\displaystyle \overrightarrow{PX} = t\vec{u},\quad t = \frac{(\vec{q}-\vec{p})\cdot\vec{u}}{\vert\vec{u}\vert^2} \,.$

From this we obtain the distance of the point

from the line by

$\displaystyle d = \frac{\left\vert(\vec{q}-\vec{p})\times\vec{u}\right\vert} {\vert\vec{u}\vert}\, .$

$\includegraphics[width=12cm]{a_abstand_punkt_gerade_bild}$

Example:

automatically generated 3/28/2008

Distance Point - Line