用平面的法向量求空间角与距离(高二、高三)

• 作 者: 成玉华
• 机 构: 山东省博兴第一中学 256500
• 出 处: 数理天地(高中版)
• 发表日期: 2005年04期
• 关键词: 法向量 向量和 距离问题 异面直线 高考题 垂线段 正三棱柱 空间直角坐标系 第二障碍 第一障碍

在历年的高考题中,立体几何部分考查最多的便是空间中的角与距离问题,自高中新教材试用以来,向量已成为了人们解立体几何题的有力工具.在教材第二册(下B)中有这样一句话:“如果α⊥α,那么向量α叫做平面α的法向量”.在教材和教师数学用书中有关平面法向量的介绍,仅此一句,易让人忽略.然而,它在解决空间中的角与距离问题中,却十分有用.

In the college entrance examination questions of the calendar year, the most studied part of the three-dimensional geometry is the angle and distance problem in space. Since the trial of the new high school textbooks, the vector has become a powerful tool for people to solve three-dimensional geometric problems. In B) there is such a sentence: “If α ⊥ α, then the vector α is called the normal vector of the plane α.” In the textbook and the teacher’s math book, the introduction of the plane normal vector, only this sentence, easy to let people ignore. However, it is very useful in solving the problem of angle and distance in space.