Mercedes-Benz theorem of plane vector: It is derived because its geometric representation resembles the symbol Mercedes-Benz, and the specific contents are as follows: There is △ABC, and point P is a point in a triangle (equinox formula on the side of the triangle). And then SA PA+SB PB+? SC PC = 0, where: SA is the area of △BCP, SB is the area of △ACP, and SC is the area of △ABP.

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.

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.

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.