First sequence for make any faces or objects to be parallal (who have themselves 3 rotations in the space! )

the Line-line + helpers line are sufficient

The 2 objects have now parallal base's faces!



Second sequence for past anywhere Base / base faces' objects
Now the objects will be perpendicular / Base/base with any orientation wanted
(mouse must on the face or parameter of the Base's target object! )



I will send in a moment the result with your object! ;)
http://moiscript.weebly.com/uploads/3/9/3/8/3938813/michael_orient.3dm

Ps the little "cutting square" on the yellow object is not 90° so perspective error can be seems exist! ;)