How this calculator works
The intersection direction is perpendicular to both plane normals, so it is their cross product. A point on the line is obtained by solving the two plane equations with the additional condition that the point is perpendicular to the line direction. Normals are scaled to unit length first. A relative tolerance of 1e-12 treats nearly parallel normals as parallel; very ill-conditioned inputs should be checked with exact arithmetic.
Formula
d = n1 cross n2. For unit normals u, v and plane constants c1, c2 in u dot X = c1 and v dot X = c2, P = ((c1 v - c2 u) cross d)/|d|^2. X = P + t d.
Worked example
The planes x = 1 and y = 2 meet along (x, y, z) = (1, 2, 0) + t(0, 0, 1). The free parameter allows every real z value.
Advertisement
Frequently asked questions
Can two planes meet at one point?
Two distinct planes in ordinary 3D space meet along a line or are parallel. A single isolated point is not possible.
Why is the point different from my answer?
An intersection line contains infinitely many points. Any one of them is a valid starting point.
What if the normals are parallel?
The planes are either identical or disjoint. The relationship output distinguishes these cases within the stated numeric tolerance.