ACR MLG TRACK HDG DEV ON SID WITH VECTOR OUT OF SFO.

Narrative

DURING CLBOUT FROM SFO ON THE OFFSHORE 1 SID; BAY DEP ISSUED US A HDG OF 120 DEG TO INTERCEPT THE PYE 151 RADIAL AND CONTINUE ON THE RZS TRANSITION. IT WAS ONLY AS WE CONTINUED OUR TURN TO 120 DEG THAT WE BOTH REALIZED THAT WE WERE XING THE 130 (APPROX) OF PYE. CONTINUING TO A HDG OF 120 AS ASSIGNED WOULD TAKE ON A DIVERGING COURSE AWAY FROM THE 151 DEG PYE AS DEPICTED ON THE SID. SIMULTANEOUSLY; AS WE DISCOVERED THIS DISCREPANCY BAY DEP ASKED US IF WE 'WEREN'T ASSIGNED A HDG OF 210 DEG TO INTERCEPT PYE 151 DEG RADIAL?' I RESPONDED 'NO SIR; YOU GAVE US HDG 120 DEG TO INTERCEPT.' BAY DEP THEN RESPONDED; 'I GAVE YOU HDG 210 DEG TO INTERCEPT THE POINT REYES 151 DEG RADIAL; TRACK OUTBOUND AND RESUME THE SAN MARCUS TRANSITION. TURN R NOW TO 210 DEG TO INTERCEPT PYE 151 DEG.' BOTH THE CAPT AND I; HEARD; UNDERSTOOD; AND READ BACK BAY DEPS INITIAL 120 DEG HDG. I BELIEVE HAD WE BOTH BEEN MORE FAMILIAR WITH THE OFFSHORE 1 DEP AND OUR RELATIONSHIP TO POINT REYES; WE WOULD HAVE QUERIED BAY DEPS ASSIGNED HDG OF 120 DEG; AND DISCOVERED THE CTLR'S MISTAKE MUCH SOONER. MORE VERBALIZATION IN THE COCKPIT MAY AID IN THIS MATTER. AS A FINAL RESULT OF ATC'S MISSTATED VECTOR; NO CONFLICT WITH OTHER TFC OCCURRED.