Parametric form of the line

Property — Parametric form

A line through the point $\vec S_0$ with direction vector $\vec v$ is written $\vec S = \vec S_0 + \vec v\,t$, that is $\begin{cases} x = x_0+v_x t \\ y = y_0+v_y t \\ z = z_0+v_z t \end{cases}, \qquad t\in\mathbb{R}.$ The vector $\vec v$ is the “velocity” of the line: as the parameter $t$ varies the point $\vec S$ traces out the line.

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Topics: Analytic geometry in space
Concepts: Line · Line in space · Vector
Skills: Analytic geometry · Using formulae