Explain the concepts of vector algebra
Answers
A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. ... Two examples of vectors are those that represent force and velocity.
Explanation:
In mathematics, vector algebra may mean:
Linear algebra, specifically the basic algebraic operations of vector addition and scalar multiplication; see vector space.
The algebraic operations in vector calculus, namely the specific additional structure of vectors in 3-dimensional Euclidean space {\displaystyle \mathbf {R} ^{3}}\mathbf{R}^3 of dot product and especially cross product. In this sense, vector algebra is contrasted with geometric algebra, which provides an alternative generalization to higher dimensions.
An algebra over a field, a vector space equipped with a bilinear product
Original vector algebras of the nineteenth century like quaternions, tessarines, or coquaternions, each of which has its own product. The vector algebras biquaternions and hyperbolic quaternions enabled the revolution in physics called special relativity by providing mathematical models.