DEP S80 IS GIVEN VECTORS ASIDE FROM THE HEADINGS REQUIRED FOR SID. DEP CTLR WAS ATTEMPTING TO VECTOR ACR X AWAY FROM CESSNA TFC AT 5500 FT. FAILED TO ALLOW ROOM FOR ACR Y ON VECTORS BELOW ACR X AND A POTENTIAL CONFLICT ENSUED. TCASII RA RECEIVED ON ACR X.

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LOCATION: RWY 13 DEP WHITESTONE. FLEW RWY 13 DEP LGA; 175 DEGS; TURN AFTER TKOF. AT 2.5 DME STARTED TURN TO 040 DEGS. CTLR DIRECTED TURN TO 020 DEGS FOR TFC; THEN SHORTLY TO 350 DEGS FOR CESSNA TFC AT 5500 FT. LEVELED AT 5000 FT; ROLLED OUT ON 350 DEG HDG. SHORTLY AFTER STABILIZING; TCASII ANNOUNCED CLB AND COMMANDED A 1500 FPM CLB; WHICH I IMMEDIATELY COMPLIED WITH; HAND-FLYING. SCOPE WAS ON 10 MI; RED DOT WAS AT 7 O'CLOCK POS; CLOSE; -300 FT. FO SAID IT WENT TO -200 FT. FO TOLD CTLR; AND THE INTRUDER SAID; 'YES THIS IS ACR Y BEHIND ACR X;' OR WORDS TO THAT EFFECT. CTLR VERIFIED THAT WE WERE ON 350 DEGS ASSIGNED; ASKED ACR Y IF HE WAS ON THE SID; YES. CALLED LGA TRACON UPON ARR ORD; WAS TOLD THAT THE CTLR ERRED; HAD BEEN RELIEVED AND DECERTIFIED. SUPPLEMENTAL INFO FROM ACN 363345: I XMITTED THAT WE WERE RESPONDING TO A TA; ACR Y RESPONDED THAT THEY WERE THE CAUSE. THE TCASII SHOWED 200 FT; LESS THAN 1 MI. IT APPEARED THAT THE CTLR DID NOT PLAN FOR 2 DISSIMILAR TURN RATE/RADIUS AND THE ACR Y TURNED TOO CLOSE BEHIND US.