Vector Workbench
2D and 3D vectors: magnitudes, unit vectors, sums by the parallelogram rule, dot products with the angle between, cross products with the area interpretation, and both projections — drawn live. Covers §4.11.
Vectors u and v
u·v = |u||v|cos θ measures alignment (zero ⇒ perpendicular); |u×v| = |u||v|sin θ is the area of the parallelogram the two vectors span, and its direction follows the right-hand rule.