Dot product

Math

Definition

The dot product (scalar product) of two vectors is a single number found by multiplying corresponding components and summing the results. It can also be computed as the product of the magnitudes times the cosine of the angle between them, and it equals zero when vectors are perpendicular.

Examples

  • ⟨2, 3⟩ · ⟨4, -1⟩ = 2(4) + 3(-1) = 5
  • Finding the angle between two vectors using cos θ = (u · v)/(|u||v|)
  • Testing if two vectors are perpendicular: if u · v = 0, they are
Key Fact

u · v = u₁v₁ + u₂v₂ = |u||v|cos θ

Related Terms

Vector operations Parametric equations

Study This Concept

Practice dot product with free review games in these units:

Pre-Calculus Unit 6: Vectors and Parametric Equations