A FO NOTES THAT WHILE ON RADAR VECTORS THEY CHANGED HDG IN RESPONSE TO A TCAS TA.

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I WAS IN THE R SEAT AND NOT FLYING THE ACFT AT THE TIME OF THE INCIDENT. WE WERE N OF THE AIRFIELD AT 4000 FT ON VECTORS FOR THE ILS 18 LOOKING FOR THE OPTION BACK TO RADAR. I THINK WE WERE GIVEN A 035 DEG HDG AND THAT IS WHAT I THINK I REPLIED BACK TO THE CTLR. WHILE ON THE HDG; WE NOTICED ANOTHER ACFT BELOW US AT ABOUT 2 O'CLOCK POS AND APPEARED TO BE CLBING ON A COLLISION COURSE. WE TURNED R AT 4000 FT TO MAINTAIN SAFETY OF FLT AND AVOID A COLLISION. I INFORMED THE APCH CTLR OF OUR ACTIONS. HE REPLIED THAT IF ON A 355 DEG HDG THE TFC WAS NO FACTOR. HE THEN TOLD US TO TURN R TO 360 DEGS. I FOUND IT ODD TO TURN R TO 360 DEGS (NEARLY A 360 DEG TURN) AND REPLIED; L HDG 360 DEGS? HE PROMPTLY CORRECTED ME AND SAID R HDG 360 DEGS. I RESPONDED; R TURN HDG 360 DEGS FOR A 'THREE SIXTY.' WE THEN COMPLETED 2 ADDITIONAL APCHS AND THE FLT WAS OVER. I FOUND OUR PROX TO THE OTHER ACFT UNUSUAL FOR THE TERMINAL AREA. IT WAS NOT UNTIL 3 HRS AFTER LNDG WHEN THE AIRFIELD MGR CALLED; THAT I REALIZED THE SERIOUS NATURE OF THE SITUATION. WE HAD DEVIATED FROM A CLRNC (TO AVOID THE OTHER ACFT). ALTHOUGH WE DID HAVE A TA WARNING; WE COULD HAVE ASKED THE CTLR ABOUT THE IMPENDING SITUATION. CORRECT HDGS AND ALTS ARE EXTREMELY IMPORTANT; ESPECIALLY IN THE TERMINAL ENVIRONMENT. IF THERE IS EVER ANY QUESTION OR CONFUSION; ASK THE CTLR. IF THE SITUATION PERMITS; ASK THE CTLR TO RESOLVE A SITUATION BEFORE DEVIATING FROM A CLRNC AND TAKING IT INTO YOUR OWN HANDS. IN RETROSPECT; WE COULD HAVE DISRUPTED THE CTLR'S AIRSPACE WHEN WE DEVIATED BY MOVING OURSELVES AWAY FROM THE PLANNED FLT PATH. THIS TYPE OF SITUATION CAN BE PREVENTED BY BEING VIGILANT ON THE RADIOS AND USING TCAS TO ANTICIPATE SITUATIONS AND RESOLVE THEM WITH ATC BEFORE THEY ARE PERCEIVED SAFETY OF FLT ISSUES.