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# 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 equation of the line that passes through the two points with given coordinates. Simply enter coordinates of first and second points, and the calculator shows both parametric and symmetric line equations. As usual, the theory and formulas can be found below the calculator.

#### Second point

Parametric equations

Symmetric equations

### Finding equation of a line in 3d

Line in 3D is determined by a point and a directional vector. The directional vector can be found by subtracting coordinates of second point from the coordinates of first point

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

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

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

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