1. The problem statement, all variables and given/known data i was given two parametric equations of two lines in R^3 and asks me to find the isometry between one line and the other knowing that point (a,b,c) of first line is mapped in point (a',b',c') of second line. 2. Relevant equations What i have to find is a 3x3 matrix wich maps the point of the first line into the point of the second line maintaining the distance between two points of the first line and their images on the second line. 3. The attempt at a solution Trying to determine such a map caused me some troubles. I thought i should multiply the generic point of the first line with a general 3x3 matrix and impose that the image of this point is at the same distance from (a',b',c') that the first generic point from (a,b,c) but this method obviously does not work because i have a system with 9 elements to find ( the 9 elements of the matrix). For sure i'm doing something wrong but i couldn't find what. Thanks in advance for any help.