Question

Prove using vectors: If two medians of a triangle are equal, then it is isosceles.

Answer 1

Using mid – point formula of vector, we can solve this 

Let ABC be a triangle and let BE and CF be two equal medians. Taking A as the origin, let the position vectors of B and C be vector b  and vector c respectively. Then

Position vector of E = 1/2(vector C) and

Position vector of  F = 1/2(vector b)

Hence, triangle ABC is an isosceles triangle.