Tranposing two 3D coordinates onto a 2D plane?

Questions & Answers
1

I have two 3D coordinates, say (0,5,2) and (1,2,3).

From those two I want to sort of ‘rotate’ them around until both their z planes are 0, thus they become (x,y,0),(a,b,0).

What I’m thinking should be done is that I would get the direction vector between the two 3D points (1,2,3)-(0,5,2) = (x,y,z), then I’ll rotate that direction vector that will make it become (0,1,0) and using the difference in that rotation rotate the original vectors.

But I have next to no idea and i’m not even sure how I could do it the way I outlined above.

Does anyone have any ideas how I can do this?

2

Why not projecting those coordinates on the plane (x0y), or said otherwise (0,5,2) and (1,2,3) becomes (0,5,0) and (1,2,0).

If this doesn’t fit what you want, tell me and I’ll move my answer into comments.