A vector can be imagined as a line segment with an arrow. The arrow represents the direction of the vector, and the length of the line segment represents 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.
Midpoint vector expression: When m is the midpoint of BC, for any point A, there is a vector AB+ vector AC=2 vector AM (this is the formula of the old textbook, which is no longer learned in the new curriculum standard textbook).
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. ? [1] If the starting point (a) and the ending point (b) of the vector are given, the vector can be marked as AB (plus sign →) at 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 from linear algebra to get a more general concept of vector. 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, when reading on weekdays, it is necessary to distinguish what kind of concept "vector" is in the text 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.