Finding vector equations for sides of a cube

[marcusr0004]

Hi everyone, this is my first post on this website, so I'm sorry if I'm posting in the wrong place. I am stumped on a question where I have to find the equations for the vectors from the origin to the corners of the top face of a cube. I have attached the diagram that we were provided, we were also given the points B=((3.1319, 22.5477, 12.1303), D= (30.2051, 13.9229, 12.1303) and the point B'=(2.3308, 20.0329, 0.0) , which is a point on the edge of the cube connecting to B. What I need to do to move on with this question is find the coordinates of A and C somehow, which I am stuck with. I have tried using the vector BB' as the cross product of the vectors BA and BC and working backwards from there, and I have also tried using the dot products of some of these vectors to find an answer, but I haven't been able to. Any hints or help would be greatly appreciated, thanks.

 

[HallsofIvy]

I am a bit confused. One of your pictures shows a square with points marked "A, B, C, and D and the other shows points marked A and A' but there is no B'. In any case, you can use the given coordinates of points A and C to find parametric equations for line AC. Then find the midpoint of that line and the plane, through the midpoint perpendicular to the line. If you do know the coordinates of B' you can use the fact that plane ABCD is perpendicular to BB' to determine the orientation of the plane.

 

[lev888]

Let's start with the top face. It's a square in 2D. You know the end points of the diagonal - BD. How do we find the other 2 points? Consider the vector sum of the sides = the diagonal. That's one equation. The other could be the length of the side vector

 

[lev888]

Let's start with the top face. It's a square in 2D. You know the end points of the diagonal - BD. How do we find the other 2 points? Consider the vector sum of the sides = the diagonal. That's one equation. The other could be the length of the side vector

Correction: since the cube is slanted we can't throw away the z coordinate, so it's not 2D. Need another equation. Assuming we are looking for point A, how about scalar product of AB and BB' is 0?