1. Dot product as overlap
2. Projection onto a line
3. Gram--Schmidt: remove what was already explained
Drag the second vector. The app builds q₁ from a, subtracts the projection of b on q₁, and normalizes the leftover into q₂.
4. Orthogonal signals
5. High-dimensional near-orthogonality
Random unit vectors in high dimensions are usually almost perpendicular.