Question
Prove that the median to the base of isosceles triangle is perpendicular to the base.
Solution
Let ABC be an isosceles triangle with AB = AC and let AD be the median to the base BC. Then D is the middle point of BC.
Take A as origin. Let
be position vectors of B and C respectively with respect to origin A such that 
Then position vector of D w.r.t A is 
Now,
Take A as origin. Let
be position vectors of B and C respectively with respect to origin A such that Then position vector of D w.r.t A is Now,
