设相异三点A(b/a,y1),B(d/c,y2),C(b+d/a+c,y3)且b/a不等于d/c,又知向量AB=2向量AC,A.b=-dB.a=cC.b=dD.ad=bc

Question

设相异三点A(b/a,y1),B(d/c,y2),C(b+d/a+c,y3)且b/a不等于d/c,又知向量AB=2向量AC,
A.b=-d B.a=c C.b=d D.ad=bc

Answer 1

答案为B
AB=(d/c-b/a,y2-y1)
AC=((b+d/a+c)-b/a,y3-y1)
AB=2AC
d/c-b/a=2((b+d/a+c)-b/a)=2(b+d/a+c)-2b/a
d/c+b/a=2(b+d/a+c)
ad(a+c)+bc(a+c)=2ac(b+d)
aad-acd-abc+bcc=0
(a-c)(ad-bc)=0
因为ad－bc不为零
a-c=0
a=c