FLC OF A CANADAIR REGIONAL JET CL65 FAILED TO TURN AND INTERCEPT THE AIRWAY AS CLRED; CAUSING A POTENTIAL CONFLICT WITH ANOTHER ACR JET AND ATC INTERVENTION TO VECTOR THEM BACK ON COURSE.

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TAKING OFF IAD ARPT. APPROX TIME XA31. WE GOT VECTORS TO JOIN J149. THE CTLRS CHANGED OUR VECTORS 3 TIMES TO JOIN J149 -- HDG 300 DEGS TO JOIN; THEN 310 DEGS TO JOIN; AND FINALLY 330 DEGS TO JOIN. WE WERE CLBING THROUGH 6000-7000 FT WHEN WE GOT OUR LAST VECTOR. I TURNED THE HDG BUG TO 330 DEGS (WE WERE ON AUTOPLT) WITH INTENTIONS OF PRESSING THE NAV BUTTON TO CAPTURE THE RADIAL. WHEN WE ROLLED OUT ON THE 330 DEG HDG; MY ATTN GOT DIVERTED TO SOMETHING ELSE; SO I NEVER PRESSED THE NAV BUTTON. WITHIN APPROX 30-40 SECONDS; WE HAD GONE THROUGH THE RADIAL; J149; THAT WE WERE SUPPOSED TO CAPTURE. NEITHER THE CAPT NOR I SAW THIS. THEN THE DEP CTLR FOR IAD CAME ON AND ALERTED US THAT WE HAD GONE THROUGH THE AIRWAY AND TOLD US TO TURN TO A 260 DEG HDG TO REJOIN AND TO INCREASE OUR RATE OF CLB. JUST THEN; THE CTLR TOLD AN ACR Y JET TO INCREASE THEIR DSCNT. NO MENTION WAS MADE THAT THE 2 AIRPLANES WERE GETTING CLOSE. THE CTLR JUST SAID TO TAKE THESE ACTIONS. WE DID GET AN AMBER TA ALERT AND OUR TCASII DID SHOW THE ACR Y JET WITHIN 4-5-6 MI OF US. WE HAD TO GO OFF AUTOPLT TO TURN ENOUGH (INCREASE BANK); SO WE COULD BETTER AVOID ANYTHING MORE SERIOUS FROM HAPPENING. NOTHING MORE WAS SAID AND WE WERE SWITCHED TO THE NEXT CTLR. THE BIG THING THAT CONTRIBUTED TO THIS SIT WAS THE CREW'S ATTN BEING DIVERTED AWAY FROM THE FLYING AT HAND AND NOT CHKING EACH OTHER'S ACTIONS -- ESPECIALLY IN A BUSY CLASS B AREA. BTWN THE CTLR ALERTING US; TCASII; AND OUR QUICK CORRECTIVE ACTIONS HELPED MAKE THIS EVENT NOTHING MAJOR. MAYBE RELYING ON THE AUTOPLT TOO MUCH ALSO MIGHT HAVE BEEN A CONTRIBUTING FACTOR.