how sets of two points in 3-dimensional space can have a distance of 5sqrt3? A. 0 B. 1 C. 5 D. 8 E. more than 8 (A-D 具体数字不清楚。。。E应该是对的)
思路(不知道对不对): 5sqrt3 = sqrt of 75, distance between two points in 3D = sqrt [(x2-x1)^2+(y2-y1)^2+(z2-z1)^2] this means that 75 should be made up of three squares, which would be 49, 25, and 1. to get 49, 25, and 1, (x2-x1) or (y2-y1) or (z2-z1) could be either 9/-9, 5/-5, or 1/-1...given all these possibilities, there should be more than 8 sets???