Vectors Coordinates of a cube.
I have been asked to find the three dimensional coordinates of a cube which has been sunk into the ground. The ground can be considered the x-y plane. and i have been given the coordinates of two of the corners of the cube on the top face (looking down on the cube) point A = (13.0492,30.9498,9.01115) and C = (1.97687,4.68868,17.3632). it is not clear where the origin is.
Points B and D are the same height above the ground.
I started of by concluding that the z coordinates of B and D where halfway between the z co-ordinates of A and C. ( 13.181175).
I then proceeded to find the resultant vectors of AB and BC. I then proceeded with knowledge that the length of BC and AB are equal, thus using the vector length formula i was able to solve for one of the coordintes of Bx = (1102.183741 - 52.52224By)/22.14466 and i subbed this value into a dot product of AB and BC and using quadratic equation i obtained values for B coordinates. i repeated this to find the D coordinates.
D= (21.1958, 12.0503, 13.1872)
However the next task of this problem is to find the co-ordinates of the A', B' ,C' and D'. which are the points at where the cube intersects the ground. A is conected to A' and similary for the other points. This is where i have become completely stuck!!!
any help would be gratefully appreciated!!