ACR TURNS WRONG DIRECTION WHEN GIVEN VECTOR AT TKOF. MULTIPLE RWY OP PARALLEL INTERSECTING RWYS.

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I AM A NEW CAPT WITH THE AIRLINE ON THE MLG. WE WEIGHED 142000 LBS FOR TKOF WHICH IS 18000 LBS BELOW MAX GROSS WT. WHEN WE CALLED ORD GND FOR TAXI THEY ASKED IF WE COULD ACCEPT RWY 9L OR RWY 22L FOR DEP SINCE THERE WOULD BE A DELAY FOR RWY 27L. EVEN THOUGH WE WERE LEGAL FOR THE 2 SHORTER RWYS; I STILL REQUESTED THE LONGER ONE (RWY 27L) SINCE I AM STILL NEW IN THE AIRPLANE AND FELT IT WOULD BE SAFER. WE CAME OUT OF GATE AND TAXIED VIA THE STUB AND PARALLEL TO RWY 27L. ON THE RWY 27L PARALLEL; GND TOLD US TO MONITOR TWR. WHILE ON THE PARALLEL TXWY AFTER THE BEFORE TKOF CHKLIST WAS COMPLETED; I GAVE OUR TKOF BRIEFING WHICH AT THAT TIME INCLUDED RWY HDG (SINCE WE HAD RECEIVED NO OTHER HDG AT THE TIME) AND TO MAINTAIN/VERIFY 5000 FT SET IN THE ALT ALERTER. APPROX 2500 FT FROM THE APCH END OF THE RWY WE WERE GIVEN POS AND HOLD ON RWY 27L. I THEN MADE OUR BEFORE TKOF PA. APPROX 500 FT FROM THE APCH END OF THE RWY WE WERE GIVEN CLRED FOR TKOF; TURN (WE ARE NOT SURE WHICH DIRECTION THE CTLR SAID) 040 DEG HDG. (COPLT REMEMBERED STARTING TO TURN HDG KNOB L TO 040 DEGS BUT SINCE THAT WOULD BE THE LONG WAY AROUND; HE TURNED IT TO THE R; BUT SOMETHING DID NOT FEEL RIGHT.) I SAID; YES; 040 DEGS TAKES US TO OUR FIRST FIX BADGER VOR. I DID NOT REMEMBER HEARING L OR R AND SINCE THE WORD 'L' WAS NOT EMPHASIZED; I TURNED TO THE R. THE COPLT ON HIS READBACK OF THE CLRNC FOR TKOF AND ASSIGNED HDG DOES NOT REMEMBER IF HE SAID L TO 040 DEGS OR HDG 040 DEGS. HE BELIEVES HE ONLY SAID HDG 040 DEGS. ON DEP; WE STARTED A R TURN HDG 040 DEGS. 1/2 WAY THROUGH THE TURN; THE TWR CTLR ASKED IF WE WERE IN A L TURN TO 040 DEGS AND WE SAID NO. WE ARE IN A R TURN. HE TOLD US TO MAINTAIN OUR HDG AND MAINTAIN 3000 FT. (CLRNC WAS TO 5000 FT.) I SAID WE MUST HAVE MISSED THE L TURN AND WAS THERE A PROB. TWR CTLR STATED WE WENT OVER THE ARR PATH OF RWY 14R. THERE WAS NO CONFLICT; HOWEVER. HOW THIS COULD HAVE BEEN AVOIDED: 1) IF YOU HAVE A FEELING SOMETHING'S NOT RIGHT; THEN IT PROBABLY IS NOT. I.E.; COPLT TURNING HDG KNOB ONE WAY THEN THE OTHER. MAKE SURE IF THERE IS ANY QUESTION; MAKE SURE YOU QUESTION IT. 2) AS A NEW CAPT OR EVEN AN EXPERIENCED CAPT; YOU MUST ALWAYS BE AWARE OF EVERY ATC CLRNC AND MAKE SURE YOU HEAR AND UNDERSTAND IT CLRLY. 3) WHEN ATC ISSUES A TURN OF MORE THAN 180 DEGS; THE CTLR SHOULD EMPHASIZE THE DIRECTION AND 'THE LONG WAY AROUND' OR SOMETHING TO THAT EXTENT.