Shows two vectors v1 and v2 on a coordinate grid and animates a linear combination c1·v1 + c2·v2. In the independent case, the animated coefficients almost never make the sum land on the zero vector (only the trivial combination does). Then it transitions to a dependent case (v2 = 2·v1) where a nontrivial choice (c1=2, c2=-1) makes the sum exactly 0, illustrating the definition of linear independence via the canonical relation c1·v1 + c2·v2 = 0.
Responsive scaling via scale=Math.min(w,h)/240 and grid snapping to a block size g for a retro aesthetic. Animation cycles every 3.6s, easing a transition from an independent vector pair to a dependent pair. Linear combination is drawn head-to-tail plus a resulting sum arrow, with a right-side panel showing coefficients and the canonical relation.