# Equation of a line passing through two points in 3d

This online calculator finds equation of a line in parametrical and symmetrical forms given coordinates of two points on the line

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.

#### Second point

Parametric equations

Symmetric equations

### 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.

$d=[x_1 - x_0, y_1 - y_0, z_1 - z_0]$

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

$x=x_0 + (x_1-x_0)t \\\\ y=y_0+(y_1-y_0)t \\\\ z=z_0+(z_1 - z_0)t$

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

$\frac{x-x_0}{x_1-x_0}=\frac{y-y_0}{y_1-y_0}=\frac{z-z_0}{z_1-z_0}$

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PLANETCALC, Equation of a line passing through two points in 3d