WHILE GIVING INST TRAINING TO A PVT PLT APPLICANT WHO WAS UNDER A HOOD; THE INSTRUCTOR PLT ALLOWED THE ACFT TO STRAY FROM THE CLRNC FLT PATH AND CROSS OVER THE APCH OF RWY 10L. THE TRACK DEV RESULTED IN AN NMAC WITH TFC ON SHORT FINAL TO RWY 10L.

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I HAD A PVT PLT STUDENT THAT I WAS WORKING WITH IN PREPARATION FOR HIS CHKRIDE; AND WE WERE DOING SOME HOOD WORK. WE HAD BEEN CLRED FOR TKOF ON RWY 28R AND DIRECT TO THE VOR AND I HAD THE STUDENT UNDER THE HOOD. TO MY KNOWLEDGE WE WERE NOT GIVEN ANY TA'S FROM THE TWR. THE STUDENT WAS HAVING A LITTLE TROUBLE WITH HIS SCAN AND WE WERE CLBING IN THE GENERAL VICINITY OF THE VOR. AT PROBABLY 200 FT AGL HE BEGAN A R TURN TO A HDG OF 330 DEGS AND I ASKED HIM WHERE HE WAS HEADED. AT THIS POINT I BELIEVE WE WERE ABOUT 50-100 FT N OF THE RWY AT THE MOST. THE STUDENT IMMEDIATELY CAUGHT HIS MISTAKE AND TURNED BACK TOWARDS THE VOR. I THEN HEARD ANOTHER PLT TELL THE TWR THAT SOMEBODY HAD JUST ABOUT HIT HIM AND HE SHOULD GET THE CALL SIGN. THE TWR TOLD THE PLT THAT HE DIDN'T KNOW WHO IT COULD BE IT WAS NOBODY HE WAS TALKING TO. THEN THE TWR YELLED OUR CALL SIGN; 'WHAT ARE YOU DOING N OF THE RWY?' THEN HE TOLD US TO GO TO DEP. APPARENTLY ANOTHER PLANE HAD BEEN CLRED TO LAND ON RWY 10L AND WE HAD COME CLOSE TO HITTING HIM. I WOULD HAVE NOT LET MY STUDENT TURN AT ALL IF I HAD KNOWN THERE WAS OPPOSITE DIRECTION TFC. I THINK; HOWEVER; NOW; THAT MAYBE IT IS NOT SO WISE TO HAVE A STUDENT PLT UNDER THE HOOD IN A HIGH DENSITY AREA.