AIRBORNE CRITICAL BTWN A DC9 ON VECTOR TO LGA WY 31; 13 MI SE AND ACR ACFT ALSO ON VECTOR COMING RIGHT TOWARD THE DC9. THE DC9 FLC WERE IMC BUT RESPONDED TO TCASII RA. NO TA ISSUED.

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FO WAS PF. WE WERE BEING VECTORED FOR LOC 31 APCH AT LGA. ALTHOUGH THE CURRENT ATIS RPTED 033 SCATTERED; 041 BROKEN CEILINGS; WE ACTUALLY EXPERIENCED ABOUT 050 OVCST SKIES AS WE WERE VECTORED AT 4000 FT MSL FROM SW OF LGA; AND A RAGGED 035-038 OVCST CEILING N AND E OF LGA. WE WERE BEING VECTORED BY NEW YORK TRACON (FREQ 134.9) AND WERE AT 4000 FT MSL AT 180 KTS ON 150 DEG HDG. WE WERE IMC. AT APPROX XA35 OUR TCASII ALERTED US OF A TA AT OUR 12 O'CLOCK POS AND SAME ALT. THE CONTACT CONTINUED MOVING DIRECTLY AT US FROM OUR 12 O'CLOCK POS. WHEN IT WAS APPROX 3-4 NM OFF OUR NOSE; I ASKED NEW YORK APCH (134.9 WAS A TERRIBLY BUSY FREQ AS THEY WERE VECTORING ACFT TO REPOS FOR THE APCH IN USE; FROM LOC 31; TO EXPRESSWAY VISUAL 31) IF THEY HAD THE TFC AHEAD OF US AND CLOSING AT SAME ALT. NEW YORK APCH REPLIED AFFIRMATIVE AND GAVE US A L 15 DEG TURN FOR TFC. THE TFC BY NOW WAS 2 NM OFF OUR NOSE. SHORTLY AFTER ROLLING OUT ON NEW ASSIGNED HDG WE RECEIVED TCASII RA TO 'CLB; CLB.' APPROX 10 SECONDS AFTER THE RA ALERT WE RECEIVED THE TCASII 'CLR OF CONFLICT' NOTICE. UPON RECEIPT OF THE RA WE COMMENCED COMPLYING BUT DUE TO THE HIGH CLOSURE RATE AND VERY CLOSE POINT OF LATERAL SEPARATION WE RECEIVED THE 'CLR OF CONFLICT' RELATIVELY QUICKLY. FROM OUR TCASII DISPLAY I ESTIMATED THE CLOSEST POINT OF OPPOSING TFC AT 200 FT VERTLY AND 3/4 - 1 MI (TO OUR R) LATERALLY. I REMARKED TO THE CTLR THAT 'THAT WAS CLOSE.' THE CTLR SAID 'SORRY.' THE FO AND I NOTED IN THE NEXT 10-15 MINS OF 'REPOS' VECTORING THAT THE CTLR MADE A COUPLE OTHER VECTOR ERRORS ON OTHER ACFT. THE CTLR APPEARED TO BE TAXED TO THE LIMIT OF HIS SKILL LEVEL. NEW YORK TRACON IS A HIGHLY CHALLENGING TFC ENVIRONMENT; EVEN DURING OPTIMUM WX AND OPS CONDITIONS; BUT WITH MARGINAL WX AND THEN CHANGING THE APCH IN USE WITH THE AIRSPACE SATURATED MAY CAUSE SOME CTLRS TO NOT BE AS VIGILANT AND DILIGENT AS THEY SHOULD BE AND ARE CAPABLE OF. TRUST YOUR TCASII!