ACR FLT CREW REPORTS TCAS RA AT 6000 FEET ON VECTORS FOR ILS RWY 19R AT DCA NEAR FDK.

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AT 6000 FT ON VECTORS TO VISUAL APCH TO IAD RWY 19R IN THE VICINITY OF FDK; WE WERE INSTRUCTED BY ATC TO TURN FROM A HDG OF 090 DEGS TO A 150 DEG HDG TO JOIN THE RWY 19R LOC. THIS WAS AFTER A NUMBER OF VECTORS BY THE TRACON; INCLUDING 1 ACROSS THE LOC. JUST PRIOR TO INTERCEPT; WE RECEIVED A TCAS CLB RA FOR TFC AT OUR 3 O'CLOCK POS AND 500 FT BELOW US AND APPARENTLY CLBING. I INITIATED AN AGGRESSIVE PITCH UP TO FOLLOW THE GUIDANCE (2000 FPM UP). WE CLRED THE CONFLICT WITHIN A FEW SECONDS. WE WERE PREVIOUSLY ADVISED OF THE TFC AT OUR 1 O'CLOCK POS ON A PREVIOUS 150 DEG VECTOR BUT THE CTLR TURNED US L TO A 090 DEG HDG BEFORE WE COULD SPOT IT VISUALLY. THE CTLR THEN TURNED US BACK TO THE 150 DEG HDG (SEEMINGLY RIGHT AT THE TFC) AND THE CONFLICT OCCURRED. BASED ON THE CHATTER ON THE FREQ AND THE ACTIONS AND LANGUAGE OF THE CTLR; IT WAS OBVIOUS SHE WAS AT OR BEYOND HER CAPACITY TO BE SITUATIONALLY AWARE. THE CTLR WAS OVERWORKED IN MY OPINION. IN THE FUTURE; I WILL BE EVEN MORE VIGILANT WHEN IT APPEARS THE CTLR IS AT CAPACITY; ESPECIALLY WITH THIS TRACON.