Math basics › Precalculus
Vectors
Size and direction
A vector has both. Written in components ⟨a, b⟩, its magnitude is √(a² + b²) — Pythagoras again.
Adding
Add the components. Geometrically, put them nose to tail.
Dot product
a·b = a₁b₁ + a₂b₂, and it equals |a||b|cosθ. Zero means perpendicular, which is the fact you will use most.