HEADING TRACK DEV WHEN PIC OF A CE550 MISINTERPS THE DIRECTION OF TURN FOR A VECTOR ISSUED BY APCH CTLR WHILE 8 MI NW OF JFK; NY.

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WHILE BEING VECTORED FOR JFK VOR DME RWY 22L APCH; ATC INSTRUCTED US TO INTERCEPT THE VOR DME RWY 22L FINAL APCH COURSE AND SLOW TO 180 KTS. AS WE WERE SLOWING; ATC INFORMED US THAT WE WERE SIGNIFICANTLY FASTER THAN THE TFC WE WERE FOLLOWING AND THAT THIS WOULDN'T WORK. HE THEN BROKE OFF THE APCH INSTRUCTING US TO TURN TO HEADING 280 DEGS. I WAS HAND FLYING THE ACFT AND THOUGHT THAT THE APCH CTLR HAD INSTRUCTED US TO TURN L TO 280 DEGS. I QUERIED MY FO WHO TOLD ME THAT THE CTLR HAD MERELY INSTRUCTED US TO TURN TO 280 DEGS. I THEN INITIATED A R TURN TO 280 DEGS. NO SOONER HAD I ROLLED OUT ON THIS HEADING THAN THE CTLR SAID; 'DIDN'T I TELL YOU TO TURN L TO 280 DEGS?' HE SOUNDED IRRITATED. I APOLOGIZED; AT WHICH POINT HE CLRED US TO 1600 FT. HE REAFFIRMED THAT HIS PREVIOUS INSTRUCTION WAS A L TURN. HE THEN ASKED US IF WE HAD THE ARPT IN SIGHT AT 10 O'CLOCK POS. WE ACQUIRED THE ARPT VISUALLY THROUGH VERY HAZY SKIES; AND THE APCH CTLR CLRED US FOR THE VISUAL BEFORE HANDING US OVER TO JFK TWR. THE TWR CLRED US TO LAND. THOUGH WE WERE QUITE HIGH; WE COMPLETED A NORMAL LNDG WITHOUT INCIDENT. NO CONFLICT OCCURRED. THIS SIT REAFFIRMED THE NEED TO CLARIFY ANY CONFUSION ABOUT AN ATC CLRNC WITH THE CTLR; NOT WITH MY FELLOW PLT.