Line of Intersection of Two Planes Calculator
The Line of Intersection of Two Planes Calculator finds the direction vector of the line where two planes meet, using the cross product of their normal vectors. Enter each plane's normal (a, b, c).
Formula
Direction = n₁ × n₂ (cross product of the two plane normals)
- Two non-parallel planes intersect in a straight line.
- The line's direction is perpendicular to both normals, i.e. their cross product.
Normals (1,1,1) and (1,−1,2)
Inputs
- Plane 1 a: 1
- Plane 1 b: 1
- Plane 1 c: 1
- Plane 2 a: 1
- Plane 2 b: -1
- Plane 2 c: 2
Cross product = (3, −1, −2), the direction of the intersection line.
Frequently asked questions
How do two planes intersect?
Non-parallel planes meet in a line whose direction is the cross product of their normal vectors.