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