* * * Basic theorem of line vector, mathematical terminology. * * * The line vector is a parallel vector. Non-zero vectors with the same or opposite directions are called parallel vectors, which are marked as A ∨ B. Any group of parallel vectors can be moved to the same straight line, so they are called * * * line vectors. The basic theorem of * * line vector is: If a≠0, then the necessary and sufficient condition of vector B and a*** line is that there is a unique real number λ, so that B = λ a..

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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.

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

In physics and engineering, 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 the basis of a vector space to set the coordinate system, and we can also define the norm and inner product on the vector space by choosing a suitable definition, which enables us to compare abstract vectors with specific geometric vectors.