Vector Rotation and Translation to Origin

In order to complete the FABRIK node I am working on some vector math.
I need to rotate and translate two Bones so that the first of them will be in the origin ( 0,0,0 ) ,
and its .Forward and .Up Axis align with the X and Y Axis. In order to do this I think I
must rotate both bones around the first bone, until the Axis’ are aligned. And the translation
will be a simple subtraction.

However, I can’t find a way to do this rotation so that it will end up with the aligned axis’.

Any help is greatly appreciated.