Question

If D is the midpoint of the side BC of ΔABC, then show by vector method, that AB² + AC² = 2(AD² + BD²)

Answer 1

D is the mid point of BC

 

=> vector BD = vector DC

vector{AB = AD + DB = AD - BD}

vector{AC = AD + DC = AD + BD}

AB² + AC² =

vector{(AB)² + (AC)² = (AD - BD)² + (AD + BD)²}

2(vectorAD)² + 2(vectorBD) = 2(AB² + BD²)