Equation of Straight Line in Space/Symmetric Form

Theorem

Let $\LL$ be a straight line embedded in a cartesian $3$-space passing through the point $\tuple {x_1, y_1, z_1}$.

$\LL$ is expressed in symmetric form by the equation:

$\dfrac {x - x_1} l = \dfrac {y - y_1} m = \dfrac {z - z_1} n$

where $l, m, n \in \R$ are the direction ratios of $\LL$.

Proof

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Also known as

The symmetric form of an equation of a straight line in space is also known as the standard form.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): line: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): line: 2.