Vector operations

Math

Definition

Vector operations include adding, subtracting, and scaling vectors, as well as computing the dot product. Vectors are quantities that have both magnitude (size) and direction, and these operations follow specific rules different from regular number arithmetic.

Examples

  • Adding vectors: ⟨2, 3⟩ + ⟨4, 1⟩ = ⟨6, 4⟩
  • Scalar multiplication: 3⟨2, −1⟩ = ⟨6, −3⟩
  • Finding the magnitude of ⟨3, 4⟩: √(9 + 16) = 5
Key Fact

Magnitude of vector ⟨a, b⟩ = √(a² + b²)

Related Terms

Dot product Parametric equations Polar coordinates Matrix operations

Study This Concept

Practice vector operations with free review games in these units:

Pre-Calculus Unit 6: Vectors and Parametric Equations