suppose that I have coordinates of 4 points X1, X2, X3, and X4 which have form of Xi = [xi1; xi2; xi3; xi4] for i = 1~4 . Their relative position to each other never change. But the whole coordinates were rotated in some way, and now I measured the coordinates of X'1, X'2, and X'3 but not X'4. In this case how can I find the coordinates of X'4 in new 3D space? What function can I use?
+) If there is a linear transform T with 3x3 size matrix that satisfies T*[X1 X2 X3] = [X'1 X'2 X'3] then is it unique?