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异面直线间的距离是对空间两条异面直线间位置关系的定量研究,同时也是立体几何学习中的一个难点.许多同学遇到此类问题时,时常感到无从下手,下面介绍几种常见的求解方法,希能抛砖引玉. 一、垂面法 当两条异面直线a、6互相垂直时,一定存在一个平面α经过直线a且与直线b垂直,如图1所示,那么,我们只需过直线b与平面α的交点P,在平面α内作直线a的垂直线PQ,则PQ即为两异面直线的公垂线.
The distance between different straight lines is a quantitative study of the positional relationship between two lines in space, and it is also a difficult point in the study of three-dimensional geometry. When many students encounter such problems, they often feel unable to start. Here are some common ones. The method of solving, Greek hope to throw bricks and jade. First, the vertical surface method When the two different straight lines a, 6 perpendicular to each other, there must be a plane α through the straight line a and perpendicular to the line b, as shown in Figure 1, then we only It is necessary to cross the intersection point P of the straight line b and the plane α, and to make the vertical line PQ of the straight line a within the plane α, then the PQ is a straight line of two different straight lines.