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利用向量证明三点共线和四点共面问题,是现行高中教材中的基本要求.有些学生对这类问题无从下手,原因就在于对利用向量证明三点共线和四点共面的实质不理解,解决这类问题关键就是把证明三点共线和四点共面问题转化为证明向量共线和向量共面问题,其主要理论是两个定理和两个推论。
The use of vectors to prove three-point collinearity and four-point coplanarity is a basic requirement in current high school textbooks. Some students cannot start with this type of problem. The reason is to use vectors to prove the three-point collinearity and the four-point coplanarity. Without understanding, the key to solving this type of problem is to turn the proof of three-point collinear and four-point coplanar problems into proof vector collinearity and vector coplanarity. The main theories are two theorems and two corollaries.