A vector is a quantity that has both magnitude and direction. A scalar, for comparison, has only magnitude. Velocity and displacement are everyday examples of vectors. An arrow with a direction is used to draw a vector. An arrow above a letter is used as the notation for a vector. In publications, a bold letter like r is often used instead because it is easier to type.

There are two kinds of vectors. One is called a polar vector; the other is called an axial vector or pseudo-vector. They both obey vector algebra, but they have different behaviors in a symmetric transformation called space inversion. Velocity and displacement are both vectors, while angular velocity, scalars, and infinitesimal angular displacement are examples of pseudo-vectors.

Vectors also have algebraic operations. The ones used most widely are addition, subtraction, and multiplication (dot product and cross product). The set of rules for...