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|<0
则(a+λb)(λa-b)<0
λa^2-ab+λ^2ab-λb^2<0
λ|a|^2+(λ^2-1)ab-λ|b|^2<0
(√2)^2λ+(λ^2-1)*1-λ*1^2<0
2λ+λ^2-1-λ<0
λ^2-λ-1<0
(1-√5)/2<λ<(1+√5)/2
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|<0
则(a+λb)(λa-b)<0
λa^2-ab+λ^2ab-λb^2<0
λ|a|^2+(λ^2-1)ab-λ|b|^2<0
(√2)^2λ+(λ^2-1)*1-λ*1^2<0
2λ+λ^2-1-λ<0
λ^2+λ-1<0
(-1-√5)/2<λ<(-1+√5)/2
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024