Question

已知向量abc满足|a|=|b|=2,|c|=1,(a-c)(b-c)=0,则|a-b|的取值范围是?

Answer 1

简单分析一下，答案如图所示

Answer 2

(a-c)(b-c)=0---->ab-c(a+b)+c^2=0---->(ab+1)^2=[c(a+b)]^2,
(ab)^2+2(ab)+1