Question

设向量a=(cosα,sinα),向量b=(cosβ,sinβ).其中0

Answer 1

|2a+b|^2=|a-2b|^2

4a^2 +4ab+b^2=a^2-4ab+4b^2

3a^2+8ab-7b^2=0

设α-β=－θ

3a^2+8|a||b|cosθ-7b^2=0

∵a^2=1 b^2=1 |a|=1 |b|=1

∴3+8cosθ-7=0

cosθ=1/2

θ=π/3

α-β=－π/3