Hi, i have three points A',B',C' and want to find a vector passing through B' and parallel to the other two points in the plane containing these 3 points. So this how i started, A'=(9,27,-0.6) B'=(12,27,-6) C'=(19,25,-8) I found the vector AB' and AC' first. A'B'= A'-B' A'C'=A'-C' Found cross product of the two resultant vector A'B' and A'C' to get a normal vector. now using the equation a*[x – xA] + b*[y – yA] + c*[z – zA] = 0, i found the equation of the plane that contains all these 3 vectors (A',B',C'). Assuming the equation is -48x + 30y -2z = -90. Now i would like to get a vector (basically x,y,z) that is passing through B' and parallel to the line passing through A' and C'. I think, finding a line passing through the origin of of the normal vector to the plane will fetch me half the answer, but how to satisfy it to be parallel to the line A'C'