Vector: a = (a₁, a₂, a₃)

↳a = (3, 4) — 3 right, 4 up

Magnitude: |a| = √(a₁² + a₂² + a₃²)

↳|a|=√(3²+4²)=5

Addition: a + b = (a₁+b₁, a₂+b₂, …)

↳(1,2)+(3,4)=(4,6)

Dot product: a·b = a₁b₁ + a₂b₂ + a₃b₃ = |a||b|cos θ

↳(1,2)·(3,4) = 3+8 = 11

Cross product (3D): a × b is perpendicular to both

↳(1,0,0)×(0,1,0) = (0,0,1)