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