The arrow pointing formula of vector subtraction means that the arrow points from the starting point of the subtracted vector to the end point of the subtracted vector.

A vector refers to a quantity with a magnitude and a direction. It can be imagined as a line segment with an arrow. The arrow indicates the direction of the vector. The length of the line segment represents the size of the vector. Only the magnitude corresponds to the vector, and the quantity without direction is called quantity.

In physics and engineering, geometric vectors are more often called vectors. Many physical quantities are vectors, such as the displacement of an object, the force exerted on it by a ball hitting a wall and so on. On the contrary, it is scalar, that is, a quantity with only size and no direction. Some definitions related to vectors are also closely related to physical concepts. For example, vector potential corresponds to potential energy in physics. ?

The concept of geometric vector is abstracted in linear algebra, and a more general concept of vector is obtained. Here, a vector is defined as an element of a vector space. It should be noted that these abstract vectors are not necessarily represented by number pairs, and the concepts of size and direction are not necessarily applicable. Therefore, it is necessary to distinguish the concept of "vector" in the text according to the context when reading on weekdays.

However, we can still find a base of vector space to set the coordinate system, and we can also define the norm and inner product in vector space by choosing appropriate definitions, which enables us to compare abstract vectors with specific geometric vectors.

Definition of vector

In mathematics, vectors (also known as Euclidean vectors, geometric vectors and vectors) refer to quantities with magnitude and direction. It can be imagined as a line segment with an arrow. The arrow indicates the direction of the vector; Line segment length: indicates the size of the vector. The quantity corresponding to a vector is called a quantity (called a scalar in physics), and a quantity (or scalar) has only a size and no direction.

Refer to the above content: vector addition and subtraction-Baidu Encyclopedia