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《数学》第二册(下B)第51页第4题:“已知正方体ABCD—A′B′C′D′的棱长为1,求直线DA′与AC的距离。下面将从三个方面谈探究解法。一、运用“转化思想”化为易求的图形距离。由课本第49页的两条异面直线公垂线存在性的探求知:两条异面直线的距离,等于其中一条直线(a)到过另一条直线(b)且与这条直线(a)平行的平面的距离。在此基础上提出是否存在分别过两条异面直线的两个平行的平面呢?如果存在,这两个平行平面的距离与这两条异面直线的距离有何关系?据此给出求异面直线距离的思想方法吗?
Mathematical second volume (below B) page 51 item 4: "The length of the known cube ABCD-A’B’C’D’ is 1. Find the distance between the line DA’ and the AC. One aspect is to explore the solution to the problem: First, use the “distinguishing ideas” to transform the distance of the graph into the easy-to-find.From the exploration of the existence of the two perpendicular lines on the 49th page of the textbook: The distance between the lines of two different surfaces is equal to The distance between a straight line (a) and another straight line (b) and a plane parallel to this straight line (a), based on which it is proposed whether there are two parallel planes that cross two straight lines of different sides. If so, what is the relationship between the distance between these two parallel planes and the distance between these two different straight lines?