A B767-200 CREW; IN CRUISE AT FL390; WERE ISSUED A VECTOR BY ARTCC; FOLLOWED BY A TCASII RA.

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WHILE IN CRUISE FLT AT FL390; WAS GIVEN A TURN 40 DEGS TO THE L (NO REASON GIVEN). ABOUT THAT SAME TIME; WE RECEIVED A TFC TA ON THE TCASII. ATC THEN CAME BACK AND TOLD US TO MAKE IT A HARD L TURN. SINCE THE TCASII HAD ALERTED US TO THE TFC CONFLICT; THE PF (FO) DISCONNECTED THE AUTOPLT AND ROLLED INTO A 30 DEG L BANK TO AVOID THE TARGET. WE THEN GOT AN RA WITH NO GUIDANCE GIVEN ON THE VERT SPD INDICATOR (IT INDICATED ALL RED UP AND DOWN). WE SCALED DOWN TO THE 6 MI SCALE AT WHICH TIME THE TFC HAD ENTERED FROM THE 2 O'CLOCK POS AND EXITED AT THE 4 O'CLOCK POS STAYING APPROX 3-4 MI HORIZ SEPARATION. CHAIN OF EVENTS WERE: 1) ATC WAS DISTR WHEN AN ACR Y FLT RPTED ON FREQ. THEY WERE GIVEN A WRONG FREQ AND ATC WAS TRYING TO DETERMINE WHERE THEY WERE. THIS DELAYED THEM IN UNDERSTANDING THE APCHING TFC CONFLICT AND TURNING THE 2 CONFLICTING AIRPLANES. 2) ATC NEVER USED THE TERM 'TFC' TO EITHER OF THE 2 CONFLICTING AIRPLANES. THEY WERE TOO NONCHALANT. 3) ATC APPROVING WRONG ALT FOR DIRECTION OF FLT TO THE OTHER ACFT. MY PLTS UNION HAS FILED AN FOIA REQUEST TO GET ALL OF THE INFO TO INCLUDE COMS RECORDINGS FROM ZKC SO WE CAN REVIEW THEM. IT WAS DETERMINED AN ATC OPERROR BY ZKC.