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1.向量(OA*OB)=(-2sinx*cosx+cos2x)=-sin2x+cos2x=-√2*sin(2x-π/4).f(x)=-√2*sin(2x-π/4).而,x∈[0,π/2].0≤x≤π/2,-π/4≤2x-π/4≤3π/4,要使f(x)有最大值,则,sin(2x-π/4)=-√2/2.即,f(x)最大=-√2*(-√2/2)=1.要使f(x)最小值,则,sin(2x-π/4)=1.即,f(x)最小=-√2*1=-√2.2. 向量OA⊥向量OB,则有向量(OA*OB)=0,即,-√2*sin(2x-π/4)=0,2X-π/4=0,X=π/8.而,向量AB=向量(OB... |
