Well as vector object has more degrees of freedom than the orientation object its not possible to convert those directly (perhaps a direct function for that might do it) back and forth. However those functions that i named can be used to change vectors respective to the set orientation.
For example (i always forget which function did which)..
Make new vector object (0,0,1) and then unrotate (or rotate) that vector with the ships orientation and it ought to point exactly along ships front vector (with length of one). Same with (1,0,0) and (0,1,0) vectors and you get all needed coordinates needed.