A VECTOR TOWARD RISING TERRAIN AND A LATE HANDOFF CAUSE CONCERN TO A FLC ON AN IFR INSTRUMENT TRAINING FLT.

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AT LGB RECEIVED CLRNC TO FOX FIELD VIA RWY HEADING; TURN LEFT AT 800 FT HEADING 200 DEGS; RADAR VECTORS SLI-V8-V363-V186-V459-V201-PMD; DIRECT FOX 3000 FT EXPECT 10000 FT IN 10 MIN; DEP FREQ 127.2. (FLT UNDER HOOD WITH INSTRUCTOR PLT.) WHEN TURNING ONTO V363; CTLR ASSIGNED HEADING OF '330 DEG RADAR VECTORS V459.' A VECTOR OF 330 DEG WAS TOWARD MOUNTAINOUS TERRAIN ABOVE ALT OF ACFT. THE NEXT COMMUNICATION FROM CTLR WAS WHEN ACFT N OF POMONA VOR; AND THIS COMMUNICATION WAS INITIATED BY THE PIC; NOT THE CTLR. THE CTLR IMMEDIATELY HANDED US OFF TO NEW CTLR. NEW CTLR DIRECTED AN IMMEDIATE HEADING CHANGE TO 270 DEG WITH AN IMMEDIATE CLIMB TO 8000 FT FOR TERRAIN AVOIDANCE. IF WE HAD BEEN IN THE CLOUDS AND HAD NOT ESTABLISHED OUR OWN 'SAFETY FENCE' WE WOULD HAVE FLOWN INTO A MOUNTAIN AT OUR ALT AND THE ASSIGNED VECTOR. CALLBACK CONVERSATION WITH THE RPTR REVEALED THE FOLLOWING INFO: THE RPTR REVEALED THAT THERE APPEARED TO BE A LOSS OF AWARENESS ON THE PART OF THE FIRST CTLR AND NO HANDOFF WAS MADE. AFTER THE HANDOFF THE RECEIVING CTLR WAS AWARE OF THE SIT AND HAD BEEN CONCERNED ABOUT IT. THE INSTRUCTOR HAD DIRECTED A TURN AWAY FROM THE APCHING TERRAIN WITHOUT CLRNC WHILE THE SIT WAS BEING RESOLVED.