NEAR MISS RPTED BTWN CLBING ACR B747 AND UNKNOWN VFR AT 10500 FT.

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I DEPARTED JFK ON THE JFK 7 DEP; BUT SHORTLY AFTER TKOF I WAS ISSUED VECTORS. I HAD JUST PASSED 10000 FT AND WAS INCREASING AIRSPD FROM 260 KTS TO 335 KTS; WHEN ON ASSIGNED HDG OF 010 DEGS. DEP SAID THERE WAS TFC AT 10 O'CLOCK AND 10500 FT. ATC THEN SAID TURN TO 080 DEGS. THIS SEEMED WRONG TO ME (IE; IT WOULD CAUSE ME TO TURN INTO THE VFR TFC AT 10 O'CLOCK) AND I ASKED THE COPLT TO CONFIRM THE 080 DEG HDG. ATC REPLIED; 'YES; TURN TO 080 DEGS AND INCREASE RATE OF CLB.' I STARTED TO TURN TO 080 DEGS WHEN I RECEIVED A TA AND NOTICED THE TFC ON TCASII APCHING FROM THE R AT 00 ALT. TCASII THEN GAVE AN RA (CLB) AND I STOPPED THE TURN AND PITCHED UP TO COMPLY WITH TCASII RA. THE SO ADDED GAR PWR AND I HAD TO REDUCE THE PITCH ATTITUDE AS AIRSPD WAS RAPIDLY APCHING MY VZF OF 256 KTS. AS THE TARGET APCHED MY POS ON TCASII; ATC SAID TURN TO 340 DEGS AND I SAW THE TFC ON TCASII SLIDE UNDER US AT -100. I FEEL THAT ATC SHOULD NEVER HAVE TURNED US TOWARD THE VFR TFC (THEY SAID THEY TRIED TO TURN US BEHIND THE VFR TFC); BUT SHOULD HAVE LEVELED US OFF AT 10000 FT; OR HAD US DSND. WE WERE FAIRLY HVY AT 750000 LBS AND NOT VERY MANEUVERABLE; AS OUR VZF WAS 256 KTS. WE NEVER SAW THE TFC; AND MY NEAR MISS DECLARATION IS BASED ON TCASII ONLY.