Tough problem... Vectors, points, and a cube

**Problem:**

A strange building has been built to look like part of a cube sticking out of the ground. You are required to find the 3d coordinates for points B and D, given the points A(13,30,9) and C(2,4,17). Points B and D are at equal height above the ground. The ground coincides with the x,y-plane

http://i169.photobucket.com/albums/u.../vectors-1.jpg

This picture provides two views of the building.

**Relevant Equations:**

Vector properties (dot product, cross product, length of vector v = |v|.

Anyone know how to approach this?