Why should vectors be introduced into middle school mathematics?
This view is not comprehensive. Although there are many problems, vector processing is indeed simpler than synthetic geometry, but we can also find ways to deal with simpler problems with synthetic geometry. Vector is introduced into middle school because it plays an important role in mathematics. As a quantity with both direction and magnitude, vector is the most basic concept in mathematics. It plays an irreplaceable role in the development of modern mathematics. It is the basic content of basic disciplines such as algebra, geometry and functional analysis. Vector is the object of algebra. Operation and its laws are the basic research objects of algebra. Vectors can perform various operations, such as addition and subtraction of vectors, multiplication of numbers and vectors (number multiplication), quantitative product of vectors and vectors (also called point multiplication), and cross product of vectors and vectors (also called cross multiplication). These operations on vectors include three different types of algebraic operations. The operation of vectors has a series of rich operational properties. Compared with digital operations, vector operations expand the objects and properties of operations. A vector is a geometric object. Vectors can be used to represent points, lines and faces in space. If, starting from the origin of the coordinate system, the vector corresponds to the points in the space one by one; A point and a non-zero vector can uniquely determine a straight line, which passes through this point and is parallel to the given vector; Similarly, a point and a nonzero vector can uniquely define a plane passing through the point and perpendicular to a given vector. This representation is very useful in high-dimensional space and can also represent curves and surfaces. Therefore, vector can describe, depict and replace the basic research objects in geometry-points, lines and surfaces, and it is also the object of geometry research. It is important to know that vectors are the object of geometry research. In solid geometry, vectors can be used to discuss the positional relationship between points, lines and surfaces in space; Judge the parallelism and verticality of lines, lines and surfaces, and measure geometry with vectors: calculate length, angle, area, etc. With the continuous expansion of mathematical vision, this concept will give us more and more uses. Vector is a natural bridge between algebra and geometry. It doesn't need any transition. In mathematics, we have two bridges between algebra and geometry, one is vector and the other is coordinate system. The coordinate system depends on the choice of the origin. The advantage of vector is that it can be independent of the origin, and every point in space has an equal position. It does not depend on coordinates, so it is more common and important than coordinate system. On the one hand, problems in geometry can be solved by vector operation. For example, the question of whether two straight lines are perpendicular can be transformed into the question of whether the dot product of two vectors is zero, and the geometric problem is solved by algebraic method. On the other hand, for algebraic problems, geometric explanations can be given by vectors. For example, the dot product of two vectors is zero, which means that the straight lines represented by these two vectors are perpendicular to each other, and so on.