Line Intersection Planes Calculator

Line Intersection Planes Calculator

Find the line where two planes meet, including a point on the line and a direction vector.

Last updated: June 2026 | By Patchworkr Team

Plane Intersection Solver
a
b
c
d
a
b
c
d
Intersection Line
x = 1.6 + 5t, y = 1.2 + 5t, z = 0 - 5t
Point (1.6, 1.2, 0) with direction (5, 5, -5)

What Is a Line of Intersection?

When two planes are not parallel, they meet along a line. That line has a direction vector given by the cross product of the plane normals, and one point on the line can be found by solving the plane equations.

How to Find the Intersection Line

  1. Enter the coefficients for both planes in Ax + By + Cz = D form.
  2. Compute the direction vector as the cross product of the plane normals.
  3. Find one point on the line by solving a reduced 2x2 system.
  4. Write the line in parametric form using the point and direction vector.
v = n1 x n2

Worked Example

The example planes produce a line with a specific point and direction vector, shown in the result panel.

Ax + By + Cz = D

Frequently Asked Questions

What if the planes are parallel?

Parallel planes never meet, so the calculator returns an error instead of a line.

What if the planes are identical?

Identical planes overlap everywhere, so there is no unique line of intersection to report.

Does the tool accept decimals?

Yes. Any finite real coefficient is accepted, including decimal and scientific notation values.

Why do I need the right-hand side D?

The constant term is required to fully describe each plane in standard form.

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