point S is on a line. The direction vector of the line is U. So the line's equation would be

. Is it clear ? There's another line which is the line going through point S and point N. The director vector of that line is V. That line's equation is

. So there are two lines which are at an angle with each other. The angle is known. THe only thing that is not known is the X and Y coordinaties of point S , or (the same) the x + y vector components of direction vector V. If you have Vx and Vy, then you can calculate N (which is the goal), because you know the distance between S and N.