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Mathematics-Online lexicon:

Two-Point Form

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The points $ X$ 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}$ .


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\,

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  automatically generated 3/28/2008