Plane Intersection Calculator
Direction Vector: -
Point on Line: -
Angle between Planes: -°
Understanding Plane Intersections
What is Plane Intersection?
The intersection of two planes in 3D space forms a line. This line represents all points that satisfy both plane equations simultaneously.
Key Formulas
- Direction vector: d = n₁ × n₂ (cross product)
- Point on line: Solve system of equations
- Angle between planes: θ = arccos(|n₁·n₂|/(|n₁||n₂|))
- Parametric form: P(t) = P₀ + td
Properties of Plane Intersections
Geometric Properties
Line direction perpendicular to both normal vectors
Infinite length
Unique unless planes parallel
Forms dihedral angle
Special Cases
Parallel planes: No intersection
Coincident planes: Infinite solutions
Perpendicular planes: 90° angle
Three planes: Point or line
Advanced Topics
Linear Algebra
Matrix representation
Eigenvalue analysis
Null space properties
Rank conditions
Applications
Computer graphics
Robotics navigation
Architectural design
Geological modeling