## ABSTRACT

Vectors are used to represent any quantity that has both a magnitude and direction. Vectors can be added, subtracted, multiplied by a number, and flipped around so that their original direction is reversed. These operations obey the familiar algebraic laws of commutativity, associativity, and distributivity. The sum of two vectors with the same initial point can be found geometrically using the parallelogram law. Multiplication by a positive number, commonly called a scalar in this context, amounts to changing the magnitude of the vector in the sense of stretching or compressing it while maintaining its direction. Multiplication by negative numbers changes the magnitude and reverses the vector’s direction. However, vector multiplication by another vector is not uniquely defined. Instead, a number of different types of products, such as the dot product, cross product, and tensor direct product can be defined for pairs of vectors.