Vector, vector addition and subtraction, product of real number and vector, coordinate representation of plane vector, bisector of line segment, product of plane vector, distance between two points in plane, translation, sine theorem, cosine theorem and oblique triangle solution are examples.

Problems that should be paid attention to in reviewing plane vector learning [examination requirements]

(1) Understand the concept of vector, master the geometric representation of vector, and understand the concept of * * * line vector.

(2) Master the addition and subtraction of vectors.

(3) Grasp the product of real numbers and vectors, and understand the necessary and sufficient conditions for the connection of 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) Mastering the quantity product of plane vector and its geometric meaning, understanding the quantity product of plane vector can deal with the problems about length, angle and verticality, and master the conditions of vector verticality.

(6) Master the distance formula between two points on the plane, the coordinate formula of the bisector and midpoint of the line segment, and skillfully use and master the translation formula.

(7) Master sine theorem and cosine theorem, and use them to solve oblique triangle, and use calculator to solve the calculation problem of triangle solution.

Problems needing attention in plane vector learning review and the prospect of college entrance examination

Vector is a newly added content in recent years, which embodies modern mathematical thought.

Because of its "dual function" in geometric form and algebraic form, vector has become the intersection of middle school mathematics knowledge and the link to examine many contents. The college entrance examination questions mainly examine the relevant basic knowledge and highlight the instrumental role of vectors. Vector plays an important role in solving geometric problems and physical problems. In recent years, the score of vector-based college entrance examination questions accounts for about 10%.

The requirements for the examination of plane vectors are as follows: first, it mainly examines the nature, operation rules and basic operation skills of plane vectors, and examines students' mastery of the operation rules of sum, difference, multiplication and inner product of plane vectors, as well as their intuitive geometric significance and correct calculation; The second is to investigate the coordinate representation and linear operation of vectors; Third, combining with other mathematical knowledge, such as curves, series, functions, triangles, etc., are generally low-level questions.

In the science examination paper of the college entrance examination in recent four years, there are two questions every year, including four small questions, the nature and algorithm of examination vector, multiplication, product of quantity, * * * line vector and trajectory. These two problems are all based on vector form to discuss conic problems.

It can be seen that vector has risen from an auxiliary tool for solving problems to one of the indispensable tools for analyzing and solving problems. In reviewing, we should pay attention to the position of this chapter in the college entrance examination. This paper mainly solves the problems of "parallelism, verticality, fixed point and included angle" in plane geometry, analytic geometry, triangle and complex number, and can properly use vector knowledge to solve these problems. Using vectors to solve kinematics and mechanics problems in physics can not be ignored.

Problems needing attention in plane vector learning review

(1) Understand the concept of vector, master the geometric representation of vector, and understand the concept of * * * line vector.

(2) Master the addition and subtraction of vectors.

(3) Grasp the product of real numbers and vectors, and understand the necessary and sufficient conditions for the connection of 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) Mastering the quantity product of plane vector and its geometric meaning, understanding the quantity product of plane vector can deal with the problems about length, angle and verticality, and master the conditions of vector verticality.

(6) Master the distance formula between two points on the plane, the coordinate formula of the bisector and midpoint of the line segment, and skillfully use and master the translation formula.

(7) Master sine theorem and cosine theorem, and use them to solve oblique triangle, and use calculator to solve the calculation problem of triangle solution.