Question

三角形ABC中,M为BC边上任一点,N为AM的中点,向量AN=X*向量AB+Y*向量AC,则X+Y=

Answer 1

概念不清呀,过程省略向量2字：

AM=2AN=2(xAB+yAC),而：MB=AB-AM,CM=AM-AC

CM与MB是同向向量,故满足关系：MB=kCM,即：AB-AM=k(AM-AC)

即：(k+1)AM=AB+kAC=2(k+1)(xAB+yAC),即：2(k+1)x=1,2(k+1)y=k

即：x=1/(2(k+1)),y=k/(2(k+1)),故：x+y=1/(2(k+1))+k/(2(k+1))=(k+1)/(2(k+1))=1/2