向量的向量积在中学数学中的应用 摘要 向量的向量积作为中学数学知识体系的一个补充与扩展，也是大学《解析几何》这一学科整个体系的基础预备内容，学好向量积能够帮助学生做好高中与大学数学知识的衔接，顺利地度过大学适应期。本文首先简要介绍了向量积在中学数学中的应用的国内研究现状以及向量积的定义与主要性质，然后利用向量积，对于中学数学中有关立体几何的证明问题、二面角的求解问题、空间中点线面间的距离问题以及三棱锥体积的求解问题等几大类问题，给出新的解法或思路，实践证明，用向量积解决许多数学问题更具简洁性，在思考问题的维度上也具有更高层次性。最后，本文从教师如何教和学生如何学这两种角度，给出了向量积的一些教学和学习建议，为向量积引入中学数学的教学体系做出了进一步的铺垫和完善。关键词 向量积 中学数学 立体几何 二面角 三棱锥的体积 学习建议The Application of Vector Product of Vector in Middle School MathematicsAbstract As a supplement and extension of the knowledge system of mathematics in middle school, the vector product of vectors is also the basic preparatory content of the whole system of the subject of analytic geometry, learning vector product well can help students to link up their high school and College Mathematics Knowledge, and pass the college adaptation period smoothly. In this paper, we first introduce the application of vector product in middle school mathematics and the definition and main properties of vector product, some new solutions or ideas are given to the problems of proving solid geometry, solving dihedral angle, distance between point lines and surfaces in space, and solving the volume of Triangular Pyramid in middle school mathematics, it has been proved by practice that it is more concise to solve many mathematical problems with vector product, and it also has higher level in the dimension of thinking problems. Finally, this paper gives some teaching and learning suggestions of ve...
