三维向量重心怎么求？

Question

如题所述

Answer 1

设,三顶点A(x1,y1),B(x2,y2),C(x3,y3)
则重心O[(x1+x2+x3)/3,(y1+y2+y3)/3]
向量OA=[x1-(x1+x2+x3)/3,y1-(y1+y2+y3)/3]
向量OB=[x2-(x1+x2+x3)/3,y2-(y1+y2+y3)/3]
向量OC=[x3-(x1+x2+x3)/3,y3-(y1+y2+y3)/3]
则,向量OA+向量OB+向量OC
=[x1-(x1+x2+x3)/3,y1-(y1+y2+y3)/3]
+[x2-(x1+x2+x3)/3,y2-(y1+y2+y3)/3]+[x3-(x1+x2+x3)/3,y3-(y1+y2+y3)/3]
=0向量