Intersecting Planes

cults3d

In our Multivariable Calculus class, we frequently discuss intersecting planes and surfaces in considerable detail. This model has proven to be highly effective when introducing new concepts, reinforcing existing ideas, and addressing student questions. I sought a representation where the planes were not perpendicular to each other, which serves as a valuable tool for illustrating that the angle between two planes is equivalent to the angle between their corresponding normal vectors. Additionally, this model demonstrates how to determine the direction of the line of intersection using the cross product of the normal vectors, as depicted in the screenshot. The planes are relatively thick, designed to withstand repeated use and manipulation by students. Initially, I had created a more fragile model that tended to break apart quickly under handling. This model was developed with Mathematica, allowing for precise control over its dimensions and properties. For further exploration, you may also want to review my Intersecting Surfaces and Quadric Surfaces Set models.