Vector Addition

Triangle law: place tail of B at head of A; resultant R goes from tail of A to head of B.

Parallelogram law: place both tails together; R is the diagonal of the parallelogram.

R² = A² + B² + 2AB cosθ, where θ is the angle between them.

Vectors commute: A + B = B + A.

If θ = 0: R = A + B (max). If θ = 180°: R = |A − B| (min). If θ = 90°: R = √(A² + B²).