Plane vector is a quantity with both direction and magnitude in two-dimensional plane, which is also called vector in physics, as opposed to a quantity (scalar) with only magnitude and no direction. Plane vectors are represented by small arrows above A, B and C, and can also be represented by the first and last letters of vector directed line segments.

Vector development process:

As an important concept in modern mathematical physics, vector was first used by British mathematician Hamilton. Although the term vector comes from Hamilton, the idea of vector as a directed line segment has a long history. There are three main lines in the origin and development of vector theory: parallelogram law of velocity and force in physics, position geometry and geometric representation of complex numbers.

The parallelogram concept of velocity and force in physics is one of the important sources of vector theory. /kloc-After the mid-8th century, the work of Euler, Lagrange, Laplace and Cauchy directly led to the establishment of vector mechanics in the mid-9th century. At the same time, the concept of vector is one of the important basic concepts in modern mathematics, which has a profound geometric background. It begins with Leibniz's positional geometry.

Modern vector theory is based on the geometric representation of complex numbers. /kloc-in the 0/8th century, due to the use of complex numbers in some mathematical derivation, the geometric representation of complex numbers has become a hot topic. Hamilton discovered quaternions in the process of making a modular simulator of three-dimensional complex numbers. Subsequently, Gibbs and Harvey created a vector analysis system based on quaternion, which was finally widely accepted.