PA28 INSTRUCTOR AND STUDENT HAD TRACK DEV WHILE ON VECTORS IN SCT CLASS E AIRSPACE.

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ON IFR TRAINING FLT WITH A STUDENT. WE WERE INSTRUCTED BY ATC TO FLY HDG 020 DEGS AND JOIN V21. WHEN IT BECAME OBVIOUS TO THE STUDENT THAT THE 020 DEG HDG WAS NOT GOING TO GET US ONTO V21 BEFORE SLI; HE TURNED TO A HDG OF 350 DEGS. ATC NOTICED THE TURN AND ASKED WHAT HDG WE WERE FLYING. STUDENT RESPONDED 350 DEGS. WE WERE INSTRUCTED THAT OUR ASSIGNED HDG WAS 020 DEGS; AND THAT WE WERE TO JOIN V21 E OF SLI. WE TURNED BACK TO 020 DEGS IMMEDIATELY. CONTRIBUTING TO THE INCIDENT WAS THE FACT THAT THE STUDENT AND I HAD BOTH ASSUMED THAT WE WERE TO JOIN V21 W OF SLI. THE 020 DEG HDG WOULD HAVE ALLOWED US TO JOIN V21 E OF SLI; BUT NOT W OF IT. OF COURSE; WE SHOULD HAVE MAINTAINED OUR ASSIGNED HDG WHETHER OR NOT WE THOUGHT IT WOULD HAVE RESULTED IN OUR REACHING THE AIRWAY. I EXPLAINED TO THE STUDENT THE IMPORTANCE OF MAINTAINING ANY HDG ASSIGNED BY ATC. LATER IN THE FLT; WHILE AT 7000 FT; ATC DIRECTED US TO CLB TO 11000 FT. THE MEA FOR NEXT PORTION OF THE AIRWAY ROSE TO 9500 FT. IMMEDIATELY BEFORE THAT COM; WE HEARD A PIREP OF ICING IN THE CLOUDS ABOVE US AT 9000 FT. 11000 FT WOULD NOT HAVE GOTTEN US TO ON-TOP CONDITIONS. WE TOLD THE CTLR THAT WE WERE UNABLE TO CLB DUE TO THE KNOWN ICING CONDITIONS ABOVE US. WE WERE IN IMC WITH RAPIDLY RISING TERRAIN AHEAD OF US; HOWEVER. WE INFORMED ATC THAT IF WE DIDN'T BREAK OUT SOON; WE WOULD NEED TO DO A 180 DEG BACK TO VMC; OR DSND (POSSIBLY TO A LOWER MVA) OUT OF THE CLOUDS. WE EVENTUALLY BROKE OUT AND CANCELED OUR IFR FLT PLAN; PROCEEDING TO OUR DEST UNDER VFR. THE REST OF THE FLT WAS UNEVENTFUL.