已知A(0,1,1) B(2,-1,0)C(3,5,7)D(1,2,4),则直线AB和直线CD所成的角的余弦值为
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![已知A(0,1,1) B(2,-1,0)C(3,5,7)D(1,2,4),则直线AB和直线CD所成的角的余弦值为](/uploads/image/z/2765278-46-8.jpg?t=%E5%B7%B2%E7%9F%A5A%280%2C1%2C1%29+B%EF%BC%882%2C-1%2C0%EF%BC%89C%EF%BC%883%2C5%2C7%EF%BC%89D%EF%BC%881%2C2%2C4%EF%BC%89%2C%E5%88%99%E7%9B%B4%E7%BA%BFAB%E5%92%8C%E7%9B%B4%E7%BA%BFCD%E6%89%80%E6%88%90%E7%9A%84%E8%A7%92%E7%9A%84%E4%BD%99%E5%BC%A6%E5%80%BC%E4%B8%BA)
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已知A(0,1,1) B(2,-1,0)C(3,5,7)D(1,2,4),则直线AB和直线CD所成的角的余弦值为
已知A(0,1,1) B(2,-1,0)C(3,5,7)D(1,2,4),则直线AB和直线CD所成的角的余弦值为
已知A(0,1,1) B(2,-1,0)C(3,5,7)D(1,2,4),则直线AB和直线CD所成的角的余弦值为
根据题可知,AB(向量)=(2,-2,-1),CD(向量)=(-2,-3,-3),则AB(向量)点乘CD(向量)=-4+6+3=5,AB(向量)点乘CD(向量)=|AB|×|CD|×cosΦ,|AB|=√5,|CD|=√22,故cosΦ=√110/22