确切地说:正方体上的棱、面对角线,体对角线等三种线中有多少对异面直线? 解法一:这三种线可分为六种情况:棱与棱、棱与面对角线、棱与体对角线、面对角线与面对角线、面对角线与体对角线以及体对角线与体对角线等,下面就这六种情况一一加以讨论。一、正方体上的棱与棱组成的异面直线对如图1,与棱AA_1组成的异面直线对有 Specifically: How many pairs of straight lines on the cuboid, face diagonal, body diagonal, etc. in the cube? Solution one: These three lines can be divided into six kinds of situations: edges and edges, edges and Face line, edge and body diagonals, face line and face line, face line and body diagonal line, as well as body diagonal line and body diagonal line, etc., the following six cases Discuss it. 1. The opposite-straight-line pair formed by the ribs and ribs on the cube is shown in Figure 1.