O is the circum - center of triangle ABC. Vector OA = a, OB = b and OC = c.
If G is the centroid of the triangle, find vector OG in terms of a, b and c.
Vector
2013-02-22 1:41 am
回答 (1)
2013-02-23 12:38 am
✔ 最佳答案
Let AG meet BC at M , then AG : GM = 2 : 1 , BM : CM = 1 : 1.We have
.→...............→..............→......→................→.............→
AG = (2/3)AM = (2/3)(AB + AC)/2 = (1/3)AB + (1/3)AC
圖片參考：http://imgcld.yimg.com/8/n/HA04628698/o/20130222162845.jpg
∴
. →......→.....→......→..............→.............→
OG = OA + AG = OA + (1/3)AB + (1/3)AC ....→.............. →......→.............. →......→
= OA + (1/3)(OB - OA) + (1/3)(OC - OA).... →...... →......→
= (OA + OB + OC) / 3
= (a + b + c)/3
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