This paper mainly studies the properties, positional relationship and measurement of vectors and their operations, planes and straight lines, spheres and polyhedrons in three-dimensional space.
First, the main points of knowledge
1. Fundamental theorem of space vector: Understand the basic concepts of space vector, such as vector, vector length, vector direction, * * line vector, parallel vector, etc. Master the addition, subtraction, number multiplication and vector multiplication of space vectors.
2. Space vectors and geometric figures: learn the application of space vectors in geometric figures such as plane, straight line, circle, sphere and polyhedron, such as solving problems such as distance, angle and length.
3. Basic concepts of solid geometry: Understand the basic concepts in solid geometry, such as points, lines, surfaces, planes, lines, angles, circles, spheres and polyhedrons. Master the relationship and nature between them.
4. Solid geometry and space vector: Learn how to use space vector to solve solid geometry problems, such as solving the positional relationship between lines and surfaces, and solving the surface area and volume of polyhedron.
Second, examples of space vectors and solid geometry
1. Examples of Basic Theorem of Space Vector:
(1) It is proved that any two nonzero vectors A and B have a unique scalar k in three-dimensional space, so that a=kb.
(2) Given the directional quantities a=( 1, 2,3) and B = (4,5,6), find k so that a=kb.
2. Examples of space vectors and geometric figures:
(1) Know the plane ABCD, point A(-2, 1, 2), B(2, 1, 2), C (2, 1, 2), and find the normal vector of the plane ABCD.
(2) Given a straight line L: X+Y+Z = 1 and a point P (0,0,0), find the distance from the straight line L to the point P. ..
3. Examples of solid geometry and space vectors:
(1) Given a cube ABCD-A'B'C'D', find the diagonal length of the cube.
(2) Given that the center o, radius r and point A are all on the sphere, find point B on the sphere so that OA=OB.
Through the above examples, we can understand the application of space vector and solid geometry in solving practical problems and their relationship. Mastering these knowledge points can help us better solve the problems of space vector and solid geometry in high school mathematics.