In mathematics, vector algebra may mean:

• The operations of vector addition and scalar multiplication of a vector space
• The algebraic operations in vector calculus (vector analysis) – including the dot and cross products of 3-dimensional Euclidean space
• Algebra over a field – a vector space equipped with a bilinear product
• Any of the original vector algebras of the nineteenth century, including
  • Quaternions
  • Tessarines
  • Coquaternions
  • Biquaternions
  • Hyperbolic quaternions