NMAC BTWN A LOW SEL CRUISING NWBOUND AND AN SMA TWIN CRUISING EBOUND AT 4500 FT; A WRONG ALT FOR ITS DIRECTION. THE SEL RPTR INSTRUCTOR PLT DIVED THE ACFT TO PROVIDE SOME SEPARATION.

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THIS INCIDENT OCCURRED ON A VFR DAY WITH +20 SM VISIBILITY AT 4500 FT AND NO CLOUDS. WE WERE ON A VFR XCOUNTRY TRAINING FLT FROM MELBOURNE INTL TO DAYTONA BEACH INTL. 1/2 WAY THROUGH THE CRUISE PORTION OF OUR FLT; A NMAC OCCURRED WITH A WHITE AND ORANGE GA TWIN ENG AIRPLANE. THE AIRPLANE CROSSED OUR PATH (10 FT VERT; 20 FT HORIZ) FROM W TO E OR L TO R. WE HAD A GND TRACK OF 348 DEGS GIVING US OUR CRUISE ALT OF 4500 FT. OUR ALTIMETER SETTING WAS GIVEN TO US BY PATRICK APCH WHOM HAD RECENTLY RELEASED US FROM FLT FOLLOWING (INCIDENT OCCURRED IN LESS THAN 5 MINS FROM RELEASE OF PATRICK APCH). BEFORE CONTACTING DAYTONA BEACH APCH FOR FURTHER FLT FOLLOWING; WE TUNED INTO DAYTONA'S ATIS FOR INFO. THE INCIDENT OCCURRED AT THIS TIME. I USED EVASIVE ACTION (FULL FORWARD YOKE TO FLY UNDER THE OTHER AIRPLANE) AND MISSED BY A SMALL MARGIN. IN REVIEWING THE NUMBER OF ERRORS THAT LED TO THE INCIDENT; I DISCOVERED THE FOLLOWING: 1) LACK OF FLT FOLLOWING FOR ADDITIONAL COLLISION AVOIDANCE PRECAUTION. 2) CONFLICTING ACFT AT 4500 FT NOT RESPECTING THE HEMISPHERIC RULE. THE OTHER AIRPLANE WAS ON A TRACK OF DUE E WHICH SHOULD HAVE PUT IT AT AN ALT OF ODD THOUSAND +500 FT (3500 FT; 5500 FT; ETC); NOT 4500 FT. THE SIMILAR ALT MAY HAVE MADE IT MORE DIFFICULT TO SEE SINCE THE AIRPLANE WAS AT A DISTANCE ON THE HORIZON. 3) STUDENT IN THE L SEAT HAD HIS HEAD DOWN IN THE COCKPIT WORKING ON HIS NAV LOG IGNORING HIS SCANNING TECHNIQUE. THE SAFETY IMPROVEMENT I WILL RECOMMENDED TO MY STUDENTS NOW TO IGNORE THE FLT LOG COMPLETELY UNTIL FLT FOLLOWING/TA SVC HAS BEEN CONFIRMED. ONCE SVC IS CONFIRMED; CONSTANT SCANNING WILL BE DONE AT LONGER INTERVALS WITH SHORTER INTERVALS FOR THE NAV LOG. 4) MY VIEW; THE R SEAT INSTRUCTOR; WAS BLOCKED ON THE L SIDE FROM WHERE THE AIRPLANE APCHED BY THE STUDENT SITTING IN THE L SEAT. I DID NOT CATCH THE VIEW OF THE OTHER AIRPLANE UNTIL IT WAS ON THE L SIDE OF THE FRONT WINDSHIELD. 5) I WAS NOT EXPECTING OR WARY OF THE SIT THAT WAS GOING TO OCCUR. FROM MY PERSPECTIVE; WE FOLLOWED ALL FARS AND STILL THIS INCIDENT OCCURRED BECAUSE SOMEBODY ELSE WAS NOT. NO IDENT OR COM WITH THE OTHER ACFT WAS MADE.