🎬three-dimensional visualization of the cross product and the property of orthogonality

This demonstration provides a clear visual and numerical proof of the fundamental geometric property of the cross product: the resulting vector $S$ (blue) is always strictly orthogonal (perpendicular) to both of the two input vectors, $v_1$ (red) and $v_2$ (green). The animation dynamically shows the blue vector maintaining its perpendicular relationship to the everchanging plane defined by the red and green vectors. This visual confirmation is reinforced by the mathematical proof, as the script calculates that the dot products $S \cdot v_1$ and $S \cdot v_2$ consistently remain zero, while the dot product with an arbitrary third vector $v_3$ (purple) fluctuates, underscoring that the orthogonality is an intrinsic result of the cross product operation itself.

🎬Narrated Video

🎬N-Dimensional Normal Vector Demo and Electromagnetic Dual Visualization

🧵Related Derivation

🧄The Orthogonality of the Cross Product Proved by the Levi-Civita Symbol and Index Notation (OCP-LCS)

⚒️Compound Page

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