I need some help in understanding how to complete my assignment. Supposedly there's a cube 'sunk in the ground'(kind of like the Rubik's cube in the museum of Melbourne) with coordinates A,A',B,B',C,C', and D,D' of which we know only 3 coordinates: B = (3, 23, 12), B' = (2, 20, 0), D = (30, 14, 12). (the ' means the coordinate is the bottom coordinate directly below the the letter without the ') (The bottom coordinates are at the bottom of the cube that is above the ground, not the entire cube)
Visuals: https://i.stack.imgur.com/Gib8N.jpg
I know how to calculate the various side lengths using vector methods i.e
$ B-B' = |BB'|$ and $|BB'|^2+|DB|^2 = |BD|^2 $
but I'm completely lost when it comes to calculating the coordinates, and any help regarding how to understand the topic would be extremely appreciated.
The line through $B$ and $B'$ extends to a corner buried in the ground. Let's call the buried corner $B_0$. The distance from $B$ to $B_0$ is $\overline{BD}$. Once you know $B_0$, you know three corners of the cube. Now for example, the line $BC$ is perpendicular to both $B'B$ and $BD$ so you can find its direction using cross product. You already know it's length.
Then you know $\vec{BA}=\vec{BC}+\vec{BD}$ so you can find $A$. Now you know all the top vertices, and you also know $v=\vec{BB_0}$. Adding $v$ in turn to $A, C, D$ will give $A',C',D'$.