Equation of a line passing through two points in 3d

You can use this calculator to solve the problems where you need to find the line equation that passes through the two points with given coordinates. Enter coordinates of the first and second points, and the calculator shows both parametric and symmetric line equations. As usual, you can find the theory and formulas below the calculator.

Equation of a line passing through two points in 3d

First point

x

y

z

Second point

x

y

z

Calculate

Parametric equations

 

Symmetric equations

 

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Finding equation of a line in 3d

A point and a directional vector determine a line in 3D. You can find the directional vector by subtracting the second point's coordinates from the first point's coordinates.

From this, we can get the parametric equations of the line.

If we solve each of the parametric equations for t and then set them equal, we will get symmetric equations of the line.