By using formula of Dot product and Mid – point we can solve this problem. Let ABC be the triangle and D, E and F are respectively middle points of sides vector BC vector CA and vector AB. Let the perpendicular through D and E meet of O join vector OF. We are required to prove that vector OF is ⊥ to vector AB. Let the position vectors of A, B, C with O as origin of reference be vector a, vector b and vector c respectively.
