🧄How the Cross Product Relates to the Sine of an Angle

The demo application acts as a practical illustration and verification tool for Lagrange's Identity. While the detailed analysis proves the identity algebraically, the demo provides a direct, hands-on experience. It allows you to quickly input any two vectors and visually confirm that the calculated squared magnitude of their cross product is equal to the product of their individual squared magnitudes minus the square of their dot product. This functionality bridges the gap between abstract algebraic proof and concrete numerical application, solidifying your understanding of the fundamental relationship between these vector operations.

🎬Find an expression for the squared magnitude of the vector and an expression for the sine of the angle

🧄Mathematical Proof

How the Cross Product Relates to the Sine of an Angle | Proof and Derivationviadean on Notion