双重向量积展开公式的两个新证明及应用

Two New Proofs and Application of the Expansion Formula of Double Vector Product

首先对各种证明双重向量积展开公式的方法进行了简单分类总结,然后给出了两个新证明。最后,不同于解析几何教材传统的方法,在空间直线以一般方程形式给出时,应用双重向量积展开公式得到一个可以直接求出点到直线的距离公式。

Firstly,various methods to prove the expansion formula of double vector product are briefly classified and summarized,and then two new proofs are given.Finally,unlike the traditional method in analytic geometry textbook,when the space straight line is given in the form of general equation,a distance formula from point to line is obtained directly by applying the expansion formula of double vector product.