1, the modulus of the vector is also called the length of the vector or the size of the vector. For a two-dimensional vector (x, y) or a three-dimensional vector (x, y, z), the modulus of the vector can be calculated by the following formula: | v | = √ (x 2+y 2) (two-dimensional vector), | v | = √ (x 2+y 2+z 2) (three-dimensional vector).

2, said the power operation is, said the square root operation is √. Taking two-dimensional vector (3,4) as an example, calculate its modulus: | v | = √ (3 2+4 2) = √ (9+16) = √ 25 = 5, so the modulus of vector (3,4) is 5.

Definition of vector

1. In mathematics, vectors (also known as Euclidean vectors and geometric 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.

2. notation of vectors: print letters (such as a, b, u, v) in bold, and add a small arrow "→" at the top of the letters when writing. If the starting point (a) and the ending point (b) of the vector are given, the vector can be recorded as AB. In the space Cartesian coordinate system, vectors can also be expressed in pairs. For example, (2,3) in the xOy plane is a vector.

3. In physics and engineering, many physical quantities are vectors, such as the displacement of an object, the force exerted 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.

4. The concept of geometric vector is abstracted from 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.

5. When reading on weekdays, we should distinguish which concept of "vector" is mentioned in the article according to the context. 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.