A B737-800 IN CRUISE TURNED THE WRONG WAY WHEN VECTORED. ATC TURNED THEM BACK; AND IN THE TURN THEY GOT A TCAS RA. THEY CLBED TO AVOID THE CONFLICT.

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I WAS THE PF FROM BOI-ATL. IN CRUISE AT FL340 APPROX 60 MI NW OF THE RMG VOR PROCEEDING DIRECT TO RMG; I RECEIVED A VECTOR FROM ZTL TO TURN R 20 DEGS. MY FO READ BACK THE CLRNC AND WE COMPLIED. A FEW MINS LATER; ZTL SAID SOMETHING THAT I DIDN'T CATCH (I THOUGHT POSSIBLY THE CTLR SAID WE SHOULD HAVE GONE L) FOLLOWED BY A VECTOR TO 090 DEGS (APPROX 70 DEGS L). WHILE IN THE TURN (APPROX 120 DEG HDG) WE OBSERVED AN AIRPLANE CO-ALT AND SLIGHTLY R OF THE NOSE. AS WE CONTINUED THE TURN WE RECEIVED A TA AND RA (CLB) FROM THE TCAS. AS I WAS COMPLYING; THE CONFLICT WAS RESOLVED AND DEV FROM ALT WAS LESS THAN 80 FT. APPROX 2 MINS LATER; ATC ADVISED US TO CALL ZTL WHEN WE ARRIVED IN ATLANTA. I WAS INFORMED THAT WE HAD BEEN ISSUED A 20 DEG L VECTOR AND HAD DEVIATED. WHILE I SPECIFICALLY REMEMBER VERBALIZING 20 DEGS R; I CANNOT REMEMBER THE FO'S READBACK. THERE APPEARED TO BE NO CONFUSION WITH THE INITIAL VECTOR. AT THE TIME OF THE INITIAL VECTOR; NEITHER OF US WERE INVOLVED WITH OTHER ACTIVITIES AND I DON'T RECALL ANY RADIO DIFFICULTIES. AT THIS TIME; I DO NOT HAVE RESULTS OF ATC INVESTIGATION. SUPPLEMENTAL INFO FROM ACN 699613: FLT WAS AT FL340. ZTL GAVE US A VECTOR OF 20 DEGS TO THE R. THE PNF READ BACK 20 DEGS R. THE PF TURNED THE ACFT 20 DEGS R. A FEW MINS LATER; THE CTLR GAVE US A HDG OF 20 DEGS L; THEN A TURN TO 090 DEGS (FROM A HDG OF APPROX 130 DEGS). IN THE TURN WE RECEIVED A TA AND WERE ABLE TO PICK UP THE TFC VISUALLY; THEN AN RA OCCURRED. NO EVASIVE ACTION WAS NECESSARY. THE CAPT CALLED ATC (ZTL) ONCE WE GOT ON THE GND. THEY SAID THEY GAVE US A 20 DEG TURN TO THE 'L' AND WE READ BACK '20 DEGS TO THE L.' CONTRIBUTING FACTORS: 1) ACFT WAS AT FL340 HDG IN AN EASTERLY DIRECTION. 2) INCIDENT HAPPENED NEAR ONE OF THE BUSIEST ARPTS IN THE WORLD.