🎬Parallelogram Diagonals Orthogonality Demo

The animated demo powerfully visualizes the fundamental principle that the diagonals of a parallelogram, represented by $v+w$ and $v-w$ , are orthogonal if and only if the adjacent sides, $v$ and $w$ , have equal magnitudes. The core takeaway is the direct correlation between the displayed metrics: the moment the magnitude of the dynamic vector $\|w\|$ crosses the fixed magnitude of $\|v\|$ , the dot product $(v+w) \cdot(v-w)$ instantly zeroes out, visually triggering the red highlight and confirming the diagonals' perpendicular intersection (90 degrees). This demonstrates that the geometric configuration required for orthogonal diagonals is the rhombus-the only parallelogram where all four sides are equal in length.