在引入空间向量后,许多空间问题(如空间角、空间距离等)的求解,已经从传统的“作—证—算”转化为将所求问题通过向量的闭回路,然后利用数量积求解,即已从传统意义上的几何方法转向以空间向量为媒介的代数运算.特别是法向量的应用,大大拓展了求解空间问题的思路.新教材在第二册 After the introduction of space vectors, the solution of many spatial problems (such as spatial angles, spatial distances, etc.) has been transformed from the traditional “doing-evidence-calculation” to a closed-loop approach to solving the problem through vectors, and then using the numerical product to solve the problem. That is to say, it has changed from the traditional geometrical method to algebraic operations using space vectors as vectors, especially the application of normal vectors, which has greatly expanded the way of solving space problems. The new textbook is in Book 2.