Principal Angles Between Planes
Compare two planes through the origin and see why their principal angles ignore the signs of their normals.
Free theory articleCompare two planes through the origin and see why their principal angles ignore the signs of their normals.
Concept & interpretation
The principal angles between two subspaces generalize the concept of an angle between two vectors. For two 2D subspaces (planes) in ℝ3, there are two principal angles. If the planes are defined as the orthogonal complements of nonzero normal vectors u and v, the principal angles describe their geometric relationship.
Interactive Experiment
Open the interactive module to visualize the planes and their normal vectors.
- Adjust the sliders for Normal u1, Normal u2, and Normal u3 to define the normal vector of the first plane.
- Adjust the sliders for Normal v1, Normal v2, and Normal v3 to define the normal vector of the second plane.
- Observe the calculated Principal Angles, Intersection Dim, and Nontrivial Cosine in the Results panel.