ALERT ARTCC RADAR CTLR CATCHES FLC DEV. HDG TRACK DEV.

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AFTER PASSING LLC VOR I SET 067 DEGS IN OBS INSTEAD OF 054 DEGS DUE TO MISREADING CHART. APPROX 36 DME ATC ISSUED A L 15 DEG TURN AND CLRED US TO GO DIRECT BAM. VERY SHORTLY AFTER WE GOT A 'TFC; TFC' ON THE TCASII. SHORTLY AFTER THAT WE GOT AN RA TO 'CLB; CLB.' THE FO FOLLOWED THE RA; CLBING 300 FT. FO SAW TFC PASS BELOW US APPROX 1000 FT AT WHICH TIME THE TCASII RPTED 'CLR OF CONFLICT.' THERE WERE NO ATC ADVISORIES ISSUED DURING THIS TIME AND WHEN WE ASKED THE CTLR IF THERE HAD BEEN A CONFLICT HE TOLD US THERE HAD BEEN NO CONFLICT. NO OTHER COMS ABOUT THIS EVENT WERE MADE BY ATC. THE CTLR ASKED US ABOUT OUR CLRNC AND I TOLD HIM WE WERE CLRED ON J-32. THERE WERE NO FURTHER DISCUSSIONS WITH ATC. THE TYPE OF MIL ACFT INVOLVED IS UNKNOWN TO ME. THE FO HAS NO MIL BACKGND AND ONLY DESCRIBED IT AS 'A BIG GRAY MIL LOOKING AIRPLANE.' AFTER SOME THOUGHT ABOUT THE NEAR MISS MY PERCEPTION IS THAT THIS MIL ACFT MAY HAVE POPPED UP OUT OF THE NEARBY MOA AND TAKEN A STAFFING RUN ON US. THE CLOSURE AND THE ABRUPTNESS OF THE TCASII RA WAS NOT WHAT I WOULD CONSIDER THE NORMAL SPD RANGE. I FIND IT ODD THAT ATC NEVER CALLED OUT ANY TFC NOR MENTIONED ANY AFTER WE ASKED ABOUT A POSSIBLE CONFLICT. THE CTLR JUST SAID THAT WE WERE GETTING CLOSE TO SOME RESTR AIRSPACE. SUPPLEMENTAL INFORMATION FROM ACN 266092: I CHKED THE CHART AND SELECTED THE PROPER RADIAL FROM THE VOR. ABOUT 3 MINS LATER THE CAPT CHKED HIS CHART AND SAID THE PROPER RADIAL IS 15 DEGS TO THE R. I LOOKED DOWN AGAIN AT MY CHART; CHKED THE VOR; AND THE JET AIRWAY NUMBER AGREED WITH HIM. I WAS AHEAD OF THE ACFT POS. I FEEL THAT I HAD CONTRIBUTED TO THIS INCIDENT BY NOT RECHKING MY POS AND LOOKING AT THE VOR FREQ ON THE JCT AIRWAY. ALSO; I DID NOT KEEP TRACK OF MY FLT PLAN TIMES ENRTE. I ALLOWED MYSELF TO BE INFLUENCED OUT OF THE RIGHT COURSE BELIEVING I WAS WRONG. I SHOULD HAVE BEEN MORE AWARE OF MY EXACT POS.