What is the equation for a 3D line?

Just like we have the equation $y=mx+b$ for $\mathbb{R}^{2}$, what would be a equation for $\mathbb{R}^{3}$? Thanks.


Here are three ways to describe the formula of a line in $3$ dimensions. Let’s assume the line $L$ passes through the point $(x_0,y_0,z_0)$ and is traveling in the direction $(a,b,c)$.

Vector Form


Here $t$ is a parameter describing a particular point on the line $L$.

Parametric Form


These are basically the equations that result from the three components of vector form.

Symmetric Form


Here we assume $a,b,$ and $c$ are all nonzero. All we’ve done is solve the parametric equations for $t$ and set them all equal.

Source : Link , Question Author : Ovi , Answer Author : Jared

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