B-777 TCASII TA RA HAD NMAC WITH B-767. VISUAL SEPARATION USED SEE AND AVOID CONCEPT IN CLASS B AIRSPACE.

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THE PROB AROSE DURING A RWY 13L DEP FROM BOEING FIELD WHEN THE DEP CTLR POINTED OUT ANOTHER ACFT; AN ACR 767 CLBING OUT OF SEATAC ARPT SBOUND; AND ASKED US IF WE HAD VISUAL CONTACT. WE DID AND SO ADVISED. THE CTLR THEN ASKED US TO MAINTAIN VISUAL SEPARATION WITH THAT ACFT DURING THE CLB BUT THEN UNEXPECTEDLY AND IMMEDIATELY GAVE US A HDG THAT WOULD PUT US ON A PERFECT HEAD-ON COLLISION COURSE WITH THAT ACFT. THE ALTS AND CLB RATES OF BOTH ACFT WERE VERY SIMILAR. OUR DESIRED RTE WAS WBOUND AND THE ACR 767 WAS TURNING EBOUND. THE ALT AND RELATIVE POS OF THE 767 WAS MONITORED ON THE TCASII DISPLAY. I COULD SEE A CONFLICT DEVELOPING AS WE TURNED TO THE REQUESTED HDG. THE FAA FLT TEST PLT WAS THE PF AT THE TIME THROUGH THE AUTOPLT. I THEN ASSUMED MANUAL CTL FO THE AIRPLANE AND INCREASED THE RATE OF CLB SEVERAL THOUSAND FPM SO AS TO PASS ABOVE THE 767. SHORTLY AFTER THAT; A TA WAS ISSUED BY TCASII. WITHIN A FEW SECONDS A PREVENTATIVE RA WAS ISSUED; WHICH CAME OUT AS AN AURAL WARNING 'MONITOR VERT SPD.' THE CORRESPONDING PITCH LIMIT INDICATION ON THE PRIMARY FLT DISPLAY (PFD) TO AVOID THE OTHER ACFT WAS TO MAINTAIN A PITCH ATTITUDE NO LOWER THAN ABOUT 15 TO 20 DEGS NOSE UP. THE RA DID NOT REQUIRE ANY ADDITIONAL MANEUVERING OR ANY DEV FROM OUR CLRNC. WE HAD TO MAKE A VERY RAPID CLB TO OUR ASSIGNED ALT OF 9000 FT MSL TO AVOID THE 767. I'M A LITTLE UNCERTAIN WHAT THE CREW OF THE 767 WERE TOLD ABOUT THE SEPARATION GIVEN TO THEM. IF THEY WERE ALSO MAINTAINING VISUAL SEPARATION; THEN PERHAPS THEY WERE ALSO EXPEDITING THEIR CLB TO AVOID US. I DON'T KNOW. IN THE FUTURE; I WON'T BE SO QUICK TO VOLUNTEER TO DO THE VISUAL SEPARATION FUNCTION; ESPECIALLY WHEN A CONFLICT CAN BE SEEN IN THE MAKING. DOES ACCEPTING RESPONSIBILITY FOR VISUAL SPN ALLOW YOU TO DISREGARD SUBSEQUENT RADAR VECTORS? WILL ATC GIVE THE 2 ACFT INVOLVED THE SAME 'MAINTAIN VISUAL SEPARATION' CLRNC? ATC SHOULD NOT BE PROVIDING VECTORS THAT CREATE A RISK OF COLLISION THAT THE PLT THEN HAS TO RECOVER FROM. 2 ACFT BOTH CLBING AND TURNING TOWARDS A HEAD-ON ENCOUNTER MAKE IT DIFFICULT TO JUDGE WHAT EVASIVE ACTION MIGHT BE REQUIRED TO 'MAINTAIN VISUAL SEPARATION.'