本文介绍并证明一个有关重心的定理,然后应用这个定理解决几个问题。定理设G是△ABC的重心,p是空间上任意一点,则 PG~2=2/3(PA~2+PB~2+PC~2)-1/9(AB~2+IC~2+CA~2)(1) 证明这里我们应用向量的方法证明本定理如下:∵ PG=PA+AG=PB+BG=PC+CG This article introduces and proves a theorem about the center of gravity, and then applies this theorem to solve several problems. Theorem Let G be the center of gravity of △ABC, p is any point in space, then PG~2=2/3(PA~2+PB~2+PC~2)-1/9(AB~2+IC~2+ CA~2) (1) Prove that we apply the vector method here to prove this theorem as follows: ∵ PG = PA + AG = PB + BG = PC + CG