首先|b|=(1+4)^(1/2)=(5)^(1/2)
计算a与b的内积:a.b=1*sinθ+2*(cosθ-2sinθ)=2*cosθ-3*sinθ
因为a.b=|a|*|b|*cosθ
=>2*cosθ-3*sinθ=5*cosθ
=>sinθ=-cosθ
|a|=(sinθ^2+cosθ^2-4sinθcosθ+4sinθ^2)^(1/2)
=(1+4sinθ^2-4sinθcosθ)^(1/2)=(1+8sinθ^2)
=>sinθ^2=1/2
因为θ在(0,π)=> sinθ>0 =>sinθ=(1/2)^(1/2),cosθ=-(1/2)^(1/2)
=>θ=3π/4