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问题如图1,一个正方体的8个顶点能连成多少对异面直线?解法1分类讨论可能的情况.(1)两条直线均为正方体的棱.以直线AD为例,与直线AD异面的正方体的棱所在直线有BB1、CC1、A1B1、C1D1四条.同理,与正方体其余的11条棱异面的棱各自都有4条,但每一对在计算时都被算了两次,所以这种情况有N1=12×(12×4)=24对.(2)一条直线为正方体的棱,另一条直线为正方体的面对角线.以直线AD为例,与直线AD异面的正方体的
The problem is shown in Fig.1. How many vertices of a cube can connect into a straight line? How to solve the problem? (1) The two straight lines are the edges of the cube, taking the straight line AD as an example, There are four lines BB1, CC1, A1B1 and C1D1 on the straight line of the square of the cube, and there are 4 bars each with the other 11 cube edges on the cube, but each pair is calculated twice , So this case has N1 = 12 × (12 × 4) = 24 pairs. (2) One straight line is the edge of the cube and the other one is the square diagonal of the cube. Take the straight line AD as an example, Square