关于空间向量外积的教学思考  

On the Teaching of Exterior Product of Spacial Vectors

作　　者：裴玉峰 陈晓煜 PEI Yufeng;CHEN Xiaoyu(Department of Mathematics,Huzhou University,Huzhou Zhejiang 313000,China;Department of Mathematics,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]湖州师范学院理学院数学系,浙江湖州313000 [2]上海师范大学数理学院数学系,上海200234

出　　处：《大学数学》2024年第2期63-67,共5页College Mathematics

基　　金：国家自然科学基金面上项目(11971135)。

摘　　要：空间向量的外积是解析几何教学的难点.这篇文章首先证明外积的代数定义与几何定义等价,然后给出不依赖坐标系选取的双重外积公式证明.这种方法揭示了公式的发现过程,希望对教学有帮助.The exterior product of spacial vectors is a difficulty in analytic geometry teaching.This paper first proves the equivalence between the algebraic definition and the geometric definition of the exterior product,and then gives a proof of the double exterior product formula that does not depend on the choice of coordinates.This approach reveals the discovery process of the formula and is hoped to be helpful for teaching.

关 键 词：外积 右手系法则 双重外积公式 

分 类 号：O13[理学—数学]