A vector, as defined below, is a specific mathematical structure. It has numerous physical and geometric applications, which result mainly from its ability to represent magnitude and direction simultaneously. Wind, for example, had both a speed and a direction and, hence, is conveniently expressed as a vector. The same can be said of moving objects and forces.
Vectors are quite useful in simplifying problems from three-dimensional geometry.
A vector of dimension n is an ordered collection of n elements, which are called components . In typewritten work, a vector is usually given a bold letter, such as A , to distinguish it from a scalar quantity, such as A . In handwritten work, writing bold letters is difficult, so we typically just place a right-handed arrow over the letter to denote a vector. The first vector has components 2 and -5. Two vectors are equal if their corresponding components are equal.