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Mathematics-Online course: Prepcourse Mathematics - Linear Algebra and Geometry - Lines and Planes

Point-Slope Form

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The points $ X$ on a line through $ P$ in direction $ \vec{u}$ can be described in parametric form by

$\displaystyle \overrightarrow{PX} = t\vec{u},\quad t\in\mathbb{R}\,. $

\includegraphics[width=8cm]{a_punkt_richtungsform_bild}

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

$\displaystyle x_i = p_i + tu_i,\quad i=1,2,3\, . $

The figure illustrates the parametric form of a line through point $ P=(1,3)$ in direction $ \vec{u}=\left(\begin{array}{c}2\\ -1\end{array}\right)$ . The point $ X$ corresponds to the parameter value $ t=3/2$ .

\includegraphics[width=12.4cm]{b_punkt_richtungsform_bild}
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  automatically generated 9/18/2007