Question

设平面向量a b的夹角为45度,且|a|=√2 |b|=1 ,若a+ λb与 λa-b的夹角是钝角则实数λ的取值范围为?

Answer 1

cos(a,b)=a*b/|a|*|b|=√2/2

a*b=√2/2*|a|*|b|=1

因为a+ λb与 λa-b的夹角是钝角

则

cos(a+λb,λa-b)=(a+λb)(λa-b)/|a+λb||λa-b|