Mathematics-Online lexicon: Two-Point Form

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Two-Point Form

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

on a line passing through two points $P\ne Q$ can be described in the following form:

$\displaystyle \overrightarrow{PX} = t\overrightarrow{PQ}, \quad t\in\mathbb{R}\, ,$

where parameter values $t\in[0,1]$ correspond to the points of the line segment $\overline{PQ}$ .

$\includegraphics[width=8cm]{a_zwei_punkte_form_bild}$

Correspondingly, for the coordinates of the vector $\vec{x}$ we have

$\displaystyle x_i = p_i + t(q_i-p_i),\quad i=1,2,3\, .$

Example:

automatically generated 3/28/2008