已知向量a=（2cosφ,2sinφ),φ∈（π/2,π）,向量b=（0,-1）,则向量a与b的夹角

已知向量a=（2cosφ,2sinφ),φ∈（π/2,π）,向量b=（0,-1）,则向量a与b的夹角

【1】可设两个向量a,b的夹角为θ,易知：0º≤θ≤180º.【2】∵向量a=(2cosψ,2sinψ).向量b=(0,-1).∴|a|=2,|b|=1.且a·b=-2sinψ.又cosθ=(a·b)/(|a|×|b|).∴cosθ=(-2sinψ)/2=-sinψ.即有：cosθ=-sinψ.【3】由题设可知：ψ∈(π/2,π),即π/2＜ψ＜π.∴0＜sinψ＜1.∴-1＜-sinψ＜0.∴-1＜cosθ＜0.结合0≤θ≤π,可知：π/2＜θ＜π.【4】∵cosθ=-sinψ.∴cos(π-θ)=sinψ=cos[(π/2)-ψ]=cos[ψ-(π/2)].即有：cos(π-θ)=cos[ψ-(π/2)].由π/2＜θ＜π,且π/2＜ψ＜π可知：0＜π-θ＜π/2.且0＜ψ-（π/2)＜π/2.∴π-θ=ψ-(π/2).∴θ=(3π/2)-ψ.即两个向量a,b的夹角为(3π/2)-ψ.∴选A.======以下答案可供参考======供参考答案1:设向量a与b的夹角为θ．a·b=-2sinφ|a|·|b|=sqrt[(2cosφ)²+(2sinφ)²]×1=2∴cosθ=(a·b)/(|a|·|b|)=-sinφ又∵φ∈(π/2,π)而θ∈(0,π)∴θ=3π/2-φ选A．供参考答案2:Men now affect all aspects of life the Internet, SNS community site to carry out is in full swing. All net, happy network competing market, investment in social networking sites passion, a small amount of financing growth of SNS website from time to time, SNS showed a feudal disputes scenes, the industry that, after the SNS community site in a good situation under , hidden deep crisis, the industry reshuffle is inevitable. SNS community site so the face of the situation, how to stand tall talent, is now anxious to deal with industry results. After I investigated a number of SNS contacts and websites, and according to some expert advice and ideas, summed up some tentative ideas, detailed tables are now the following three aspects:First, take the vertical to carry out the Road: refining market, segment usersAlthough China's SNS industry to carry out faster, but slower than the four seas, the prevalence of market simulation, learning, and homogenization, which will make a large minority of the Chinese Internet industry is facing serious results, the user will be from the last novel, easy to gradually transformed into product claims to withstand higher, more critical,shoes nike air max, more emotional consumers who seek analysis Ereli analysis flute teacher Cao, Coupling characteristics of the Chinese market, can make differentiated SNS continued to make good business ability to carry out, SNS also stop in the industry reshuffle. Senior members of the Internet, blog, create one of China Fang Xingdong also think that the current international market competition is not enough intense SNS, which will present the homogenization of scene. On innovation, he said, carried out abroad, the vertical type SNS good analogy is worth international own. Carried out on the vertical, is not unfamiliar with the current of everyone, the industry thought, stop vertical

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