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中学立体几何课本中有这样一道例题:已知两条异面直线a、b所成的角为θ,它们的公垂线段AA′的长度为d,在直线a、b上分别取点E、F,设A′E=m,AF=n,求EF. 解题之后(如图一),它给出了一个求空间两异面直线上两点间的距离公式(以下简称距离公式): EF=(d~2+m~2+n~2±2mncosθ)~(1/2).其中,当点F(或E)在点A的(或A’的)另一侧取“+”号.这个公式有如下特殊情形:
There is such an example in the middle school textbook of three-dimensional geometry: It is known that the angles formed by the two different straight lines a and b are θ, and the length of their vertical line AA′ is d, and the points E and B are respectively taken on the lines a and b. F, set A’E = m, AF = n, find EF. After solving the problem (Figure 1), it gives a formula for the distance between two points on the straight line of two different planes (hereinafter referred to as the distance formula): EF=(d~2+m~2+n~2±2mncos[theta])~(1/2). Wherein, when the point F (or E) takes the “+” on the other side of the point A (or A’) No. This formula has the following special conditions: