Arithmetic rules add up known vectors and take any point on the plane. If solved, the vector is called sum and recorded as; The operation of finding the sum of two vectors is called vector addition The inverse quantity added by the subtraction vector is called the difference of sum; The operation of finding the difference between two vectors is called the subtraction of vectors and the product of real numbers and vectors, where when the directions are the same,; When reversed, the number of vectors
2. Important theorem, formula 1. Basic theorem of plane vectors: If there are two vectors without straight lines in the same plane, then there is only one pair of real numbers for any vector in this plane, which is the necessary and sufficient condition of 2. Two vectors are parallel: ∨If, then ∨3. Two nonzero vectors are perpendicular. Then the midpoint coordinate formula is obtained. 5. Translation formula: If the point is translated by vector, then 6. Sine theorem and cosine theorem: (1) Sine theorem: (2) Cosine theorem: 3. Learning requirements and problems needing attention 1. Learning requires (1) to understand the concept of vector and master its geometric representation. (2) Master the arithmetic and operation rules of vector addition and subtraction. (3) Master the arithmetic and operation rules of the product of real numbers and vectors, and understand the necessary and sufficient conditions of the connection between the two vectors. (4) Understand the basic theorem of plane vector, understand the coordinate concept of plane vector, and master the coordinate operation of plane vector. (5) Grasp the product of plane vectors and its geometric meaning, understand that the number of plane vectors can be used to deal with problems related to length, angle and verticality, and master the conditions of vector verticality; (6) Master the formulas of bisector and midpoint coordinates of line segments, and be familiar with the application; Master the translation formula. (7) Master sine theorem and cosine theorem, and use them to solve oblique triangles. (8) Through the application study of solving triangles, the ability to solve practical problems by using the learned knowledge is continuously improved. 2. Problems needing attention (1) The vector we study in this chapter has two elements: size and direction. When a vector is represented by a directed line segment, it has nothing to do with the position of the starting point of the directed line segment, and all directed line segments with the same direction and length represent the same vector. (2) Two basic theorems of * * * line vector and plane vector reveal the basic structures of * * * line vector and plane vector, which are the basis for further study of vectors. (3) The product of vectors is a number. When the angle between two vectors is acute, their product of quantities is greater than 0; When the angle between two vectors is obtuse, their quantitative product is less than 0; When the angle between two vectors is 90, their product is equal to 0, and the product of zero vector and arbitrary vector is equal to 0. (4) By multiplying the vectors, we can calculate the length of the vectors, the distance between two points on the plane and the included angle between the two vectors, and judge whether the corresponding two straight lines are vertical. (5) The product of quantities does not satisfy the associative law, because the result of summation is quantity, so summation is meaningless, and of course it can't be equal.
Seeking adoption is a satisfactory answer.