Find a point, a direction vector, and the parametric equations for the line where two planes meet.
Last updated: June 2026 | By Patchworkr Team
Plane 1 a is required.
The line direction comes from the cross product of the plane normals. A point on the line is found by solving the two plane equations with one variable set to zero and falling back to the other coordinate planes if needed.
For planes x = 0 and y = 0, the intersection line is the z-axis.
What if the planes are parallel?
Then there is no unique line of intersection.
Can identical planes intersect in a line?
No. Identical planes overlap completely and do not produce a unique line.
Does blank input count as zero?
No. Blank input is treated as missing, not zero.
Why not use only the direction vector?
A line needs a point as well as a direction to be fully specified.
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