A PA32 PLT NEARLY FLIES INTO THE CLASS B OF LAX BUT THE SOCAL CTLR DIRECTED HIM AWAY FROM THE AREA; VECTORS TO DEST ARPT; BUR; CA.

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WHILE RETURNING AFTER A DAY TRIP; FLYING WBOUND INTO SIGNIFICANT HAZE WITH THE SETTING SUN JUST ABOVE THE HORIZON; WE FLEW IN THE DIRECTION OF THE ARPT; WHICH IS IDENTED VISUALLY BY FLYING BTWN MOUNTAIN RIDGES. DUE TO THE EXTREMELY LOW VISIBILITY AND SUN GLARE BOTH OFF THE HAZE AND INTO THE ACFT WINDOW; THE DIRECTIONAL GYROSCOPE WAS DIFFICULT TO SEE AND THE PLT VISUALLY IDENTED THE WRONG MOUNTAIN RIDGES; SO THE ACFT FLEW ON A MORE SOUTHWESTERLY HEADING RATHER THAN DUE W. ATC NOTIFIED US THAT WE WERE APCHING LAX CLASS B AIRSPACE AND ASSIGNED A HEADING TO TAKE US DIRECTLY TOWARD BUR. WE WERE NOT TOLD WE ENTERED CLASS B AND I DON'T BELIEVE WE DID BUT IT WAS A SOBERING EXPERIENCE FOR A CAREFUL PLT. LESSONS LEARNED: WHEN FLYING INTO A HAZY BRIGHT SUNSET; IFR RATHER THAN VFR PROCS ARE MORE APPROPRIATE. IF WE HAD REQUESTED AN IFR APCH WITH VECTORS THE SUN GLARE PROB WOULD NOT HAVE BEEN A FACTOR. IF VFR IS USED; IFR PROCS (LIKE FOLLOWING A VOR RADIAL; WHICH WAS AVAILABLE) ARE USEFUL 'BACKUPS' TO VISUALLY IDENTING YOUR POS WHEN VISIBILITY IS LOW.