Math

Line of Intersection of Two Planes Calculator

Find the direction vector of the line where two planes meet.

Plane 1 a

Plane 1 b

Plane 1 c

Plane 2 a

Plane 2 b

Plane 2 c

Calculated Output

Direction x 1

Direction y -1

Direction z 1

Formula: direction = n₁ × n₂ (cross product of normals)

Step-by-Step Breakdown

1. Values used:

2. Plane 1 a = 1

3. Plane 1 b = 1

4. Plane 1 c = 0

5. Plane 2 a = 0

6. Plane 2 b = 1

7. Plane 2 c = 1

9. Direction x = Plane 1 a x Plane 1 b = 1 x 1 = 1

10. Direction y = -1

11. Direction z = Plane 1 a x Plane 1 b = 1 x 1 = 1

Did this calculator solve your problem today?

The math behind it

The line of intersection runs along the cross product of the two planes' normal vectors (a, b, c). A zero vector means the planes are parallel.

Planes x + y = d and y + z = d → direction (1, −1, 1).

What if the direction is zero?

The planes are parallel and either never meet or are the same plane.