EDIT
I don’t know is it important, but destination triangle angles may be different than these of source. Does that fact makes transformation non-affine ? (i’m not sure)

I have two triangles in 3D space. Given that i know (x,y,z) of point in first triangle and i know vectors V1,V2,V3. I need to find point (x’,y’,z’). What transformation i should do to point (x,y,z) with vectors V1,V2,V3 to get that transformed point in the second triangle ?
Thanks for help !!!
You want a matrix transformation T such that T X = X’, where X is the matrix whose columns are the co-ordinates of the vertexes of the first triangle and X’ is the same for the second triangle. Multiplying each side by the inverse of X yields T = X’ X-1.