Finding Perpendiculars

Trigonometry · Axiom Academy

Discover how to find the one vector perpendicular to two others in 3D space using the right-hand rule! The Problem: Building a Solar Panel Imagine you're installing a solar panel. You know two edges of the panel, but you need to find the direction it faces (perpendicular to both edges) to calculate sunlight exposure. In 2D, finding a perpendicular is simple—there are only two choices. But in 3D, there are infinitely many perpendicular vectors! We need a systematic way to pick one. Only 2 perpendicular directions (up or down) Infinitely many perpendicular directions! (All vectors in the circle) The right-hand rule is a simple physical gesture that always points to the perpendicular direction. Let's learn how it works! Try different vector combinations. Use the right-hand rule to predict where the perpendicular should point, then check your answer! From Hand Rule to Cross Product You've learned the right-hand rule —a physical method for finding the direction perpendicular to two vectors. This intuitive gesture is actually encoding deep mathematical relationships! Physics: Torque, angular momentum, magnetic forces Engineering: Stress analysis, robotics, structural forces Computer Graphics: Surface normals, lighting calculations, collision detection Navigation: Coordinate system transformations

This is the written version of the interactive lesson above. See the full Trigonometry course.