浅谈空间几何中向量的妙用

摘要：解析几何是近代数学的转折点, 历年高考中, 关于用向量妙解立体几何问题, 是考察的重点和热点。向量是人教版高中教材的新增内容, 它的出现,为几何问题代数化提供了很好的工具, 降低了学生对空间想象能力的要求.因此, 利用向量解决立体几何问题成了高中数学中一道靓丽的风景线, 此类问题在全国的高考中更是屡见不鲜. 本文将对空间向量的应用进行探讨, 帮助同学们进一步的理解空间向量的应用. 其中用向量代数的方法解决几何问题得到了广泛普及。法向量作为数学的一种解题工具, 为我们拓宽了解决立体几何问题的角度, 不过在法向量运用过程中, 同学们应充分挖掘其内涵, 建系要建得合理, 最好依托题目的图形, 向量的坐标才会容易求得, 再结合公式进行计算。本文着重旨在浅谈空间几何中向量的妙用, 希望为中学数学教学和学生学习提供一点有价值的参考。
关键词：向量；夹角；法向量；
On The Use of Vector in Geometric Space
Abstract: Analytic Geometry is a turning point of modern mathematics, and using vector to solve geometry problems is the focus and hot spots of study in the college entrance examination every year. Vector is an additional part in the new high school textbook output by People’s Educational Press, whose appearance provides a good tool to the issue of algebra to geometry and reduce the requirements of the students’ imaginary ability. Therefore, using vector to solve geometric problems becomes a scenic beauty in high school math teaching. Such issue is a common occurrence in our country in the college entrance examination. This paper will explore the application of vector space to help students to understand space vector better, of which using vector algebra to solve the problem have been widely spread. As a kind of mathematical problem-solving tool, law vector has broaden the perspective of three-dimensional geometry problems for us, but during the process of using vector, the students should fully tap its content and construction to build a reasonable and based on the best topic graphics, in this way, vector coordinates can be easily obtained, then combine it with formula for calculation. This paper mainly seeks to study the use of vector in geometric space, hoping to provide some valuable reference for secondary school mathematics teaching and learning.
 Key words: Vector; Angle; Law Vector;