Vector-points-angle problem

Hi all,

I have a 2 points - 1 vector - 1 angle problem in 3D:

- There are two points, S and N.

- The x,y,z-coordinates of S are known.

- Only the z-coordinate of N is known.

- The distance between N and S is known!

- there is a vector U which is the direction of a line going through S

- the vector V is the direction vector (N-S) of the points mentioned

- the angle between vector U and V is known!

Problem: calculate the other coordinates (x,y) of point N. If anybody could help me solve it, it would be greatly appreciated!!

Trying to make it more clear

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.