已知向量a,b满足:IaI=1,IbI=2,Ia-bI=根号七,求Ia-2bI
问题描述：
已知向量a,b满足:IaI=1,IbI=2,Ia-bI=根号七,求Ia-2bI
答
(a-b)²=a²-2ab+b²=1+4-2ab=7;
ab=-1;
Ia-2bI=√(a-2b)²=√(a²+4b²-4ab)=√(1+16+4)=√21;
答
|a-b|²=7
a²+b²-2a.b=7
1+4-2a.b=7
a.b= -1
Ia-2bI²
=a²-4a.b+4b²
=1+4+4*4
=21
|a-2b|=√21