已知非零向量a,b〈a,b上有箭头〉满足|a|=1且(a+b)(a-b)=1/21）若a乘b=1/2,求向量a,b的夹角

Question

已知非零向量a,b〈a,b上有箭头〉满足|a|=1且(a+b)(a-b)=1/2 1）若a乘b=1/2,求向量a,b的夹角

Answer 1

(a-b)(a＋b) = a²-b² = |a|²-|b|²=1/2
将|a|=1代入,得
|b|²=1/2
|b|=√2/2
设夹角为α,则
a·b=|a|·|b|·cosα
=1·√2/2·cosα
=1/2
cosα=√2/2
α=π/4=45º