设长方体的各棱与坐标轴平行,已知长方体的两个顶点的坐标,试写出其余六个顶点的坐标: (1)(1,1,2
设长方体的各棱与坐标轴平行,已知长方体的两个顶点的坐标,试写出其余六个顶点的坐标: (1)(1,1,2),(3,4,5); (2)(4,3,0),(1,6,-4).
(1)各棱与坐标轴平行所以(112)(345)必是长方体的两个对角顶点;与(112)相邻的顶点为:(115)(142)(312);与(345)相邻的顶点为:(342)(315)(145).
(2)各棱与坐标轴平行所以(430)(16-4)必是长方体的两上对角顶点;与(430)相邻的顶点为:(43-4)(460)(130);与(16-4)相邻的顶点为:(160)(13-4)(46-4).
(1)各棱与坐标轴平行,所以(1,1,2),(3,4,5)必是长方体的两个对角顶点;与(1,1,2)相邻的顶点为:(1,1,5),(1,4,2),(3,1,2);与(3,4,5)相邻的顶点为:(3,4,2),(3,1,5),(1,4,5).(2)各棱与坐标轴平行,所以(4,3,0),(1,6,-4)必是长方体的两上对角顶点;与(4,3,0)相邻的顶点为:(4,3,-4),(4,6,0),(1,3,0);与(1,6,-4)相邻的顶点为:(1,6,0),(1,3,-4),(4,6,-4).