🧄Verification of Orthogonal Tangent Vector Bases in Cylindrical and Spherical Coordinates

The orthogonality of basis vectors is a fundamental property of cylindrical and spherical coordinate systems. This means their basis vectors are always mutually perpendicular, a fact that is mathematically proven by their dot products consistently equaling zero. This property is critical in physics and engineering as it greatly simplifies complex vector operations and calculations.

🎬how the cylindrical and spherical basis vectors remain perpendicular to each other regardless of their position

Orthogonal coordinate systems have basis vectors that are always perpendicular to each other, regardless of the angles. This is visually represented by the dot product of any two distinct basis vectors always being equal to zero. The demo clearly shows this by calculating and displaying the dot products in real-time as you adjust the angles, demonstrating the fundamental geometric properties of cylindrical and spherical coordinate systems.

🖊️Mathematical Proof

Verification of Orthogonal Tangent Vector Bases in Cylindrical and Spherical Coordinates | Proof and Derivationviadean on Notion