作业帮已知向量a=(cos3/2x,sin3/2x)向量b=(cos1/2x,-sin1/2x)且x∈[π/2,π]问以下2问1.求向量a*向量b,│向量a+向量b│；2.求f(x)=向量a*向量b+2│向量a+b│的最小值
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![已知向量a=(cos3/2x,sin3/2x)向量b=(cos1/2x,-sin1/2x)且x∈[π/2,π]问以下2问1.求向量a*向量b,│向量a+向量b│；2.求f(x)=向量a*向量b+2│向量a+b│的最小值](/uploads/image/z/10152778-58-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28cos3%2F2x%2Csin3%2F2x%29%E5%90%91%E9%87%8Fb%3D%28cos1%2F2x%2C-sin1%2F2x%29%E4%B8%94x%E2%88%88%5B%CF%80%2F2%2C%CF%80%5D%E9%97%AE%E4%BB%A5%E4%B8%8B2%E9%97%AE1.%E6%B1%82%E5%90%91%E9%87%8Fa%2A%E5%90%91%E9%87%8Fb%2C%E2%94%82%E5%90%91%E9%87%8Fa%2B%E5%90%91%E9%87%8Fb%E2%94%82%EF%BC%9B2.%E6%B1%82f%28x%29%3D%E5%90%91%E9%87%8Fa%2A%E5%90%91%E9%87%8Fb%2B2%E2%94%82%E5%90%91%E9%87%8Fa%2Bb%E2%94%82%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC)
已知向量a=(cos3/2x,sin3/2x)向量b=(cos1/2x,-sin1/2x)且x∈[π/2,π]问以下2问1.求向量a*向量b,│向量a+向量b│；2.求f(x)=向量a*向量b+2│向量a+b│的最小值
已知向量a=(cos3/2x,sin3/2x)向量b=(cos1/2x,-sin1/2x)且x∈[π/2,π]问以下2问
1.求向量a*向量b,│向量a+向量b│；2.求f(x)=向量a*向量b+2│向量a+b│的最小值
已知向量a=(cos3/2x,sin3/2x)向量b=(cos1/2x,-sin1/2x)且x∈[π/2,π]问以下2问1.求向量a*向量b,│向量a+向量b│；2.求f(x)=向量a*向量b+2│向量a+b│的最小值
1
a·b=(cos(3x/2),sin(3x/2))·(cos(x/2),-sin(x/2))
=cos(2x)
|a+b|^2=|a|^2+|b|^2+2a·b
=1+1+2cos(2x)
=4cosx^2
x∈[π/2,π],即：cosx