求与向量a=(7/2,1/2),b=(1/2,7/2)的夹角相等,且模长为1的向量
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![求与向量a=(7/2,1/2),b=(1/2,7/2)的夹角相等,且模长为1的向量](/uploads/image/z/2476859-59-9.jpg?t=%E6%B1%82%E4%B8%8E%E5%90%91%E9%87%8Fa%3D%EF%BC%887%2F2%2C1%2F2%EF%BC%89%2Cb%3D%EF%BC%881%2F2%2C7%2F2%EF%BC%89%E7%9A%84%E5%A4%B9%E8%A7%92%E7%9B%B8%E7%AD%89%2C%E4%B8%94%E6%A8%A1%E9%95%BF%E4%B8%BA1%E7%9A%84%E5%90%91%E9%87%8F)
求与向量a=(7/2,1/2),b=(1/2,7/2)的夹角相等,且模长为1的向量
求与向量a=(7/2,1/2),b=(1/2,7/2)的夹角相等,且模长为1的向量
求与向量a=(7/2,1/2),b=(1/2,7/2)的夹角相等,且模长为1的向量
设所求向量c=(m,n),
|c|=√(m^2+n^2)=1,
设向量a和c夹角为θ
cosθ=a·c/(|a||c|=(7m/2+n/2)/[√(49/4+1/4)*1]=√2(7m/2+n/2)/5,
cosθ=b·c(/|b||c|)=(m/2+7n/2)/√[(1/4+49/4)*1]=√2(m/2+7n/2)/5,
√2(7m/2+n/2)/5=√2(m/2+7n/2)/5,
m=n,
m^2+n^2=1,
m=±√2/2,
n=±√2/2,
m,n应取同号
则向量c=(√2/2,√2/2),c=(-√2/2,-√2/2),
设所求向量c=(m,n),
|c|=√(m^2+n^2)=1,
设向量a和c夹角为θ
cosθ=a·c/(|a||c|=(7m/2+n/2)/[√(49/4+1/4)*1]=√2(7m/2+n/2)/5,
cosθ=b·c(/|b||c|)=(m/2+7n/2)/√[(1/4+49/4)*1]=√2(m/2+7n/2)/5,
√2(7m/2+n/2)/5=√...
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设所求向量c=(m,n),
|c|=√(m^2+n^2)=1,
设向量a和c夹角为θ
cosθ=a·c/(|a||c|=(7m/2+n/2)/[√(49/4+1/4)*1]=√2(7m/2+n/2)/5,
cosθ=b·c(/|b||c|)=(m/2+7n/2)/√[(1/4+49/4)*1]=√2(m/2+7n/2)/5,
√2(7m/2+n/2)/5=√2(m/2+7n/2)/5,
m=n,
m^2+n^2=1,
m=±√2/2,
n=±√2/2,
m,n应取同号
则向量c=(√2/2,√2/2), c=(-√2/2,-√2/2),
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