Question
Using vectors, prove that if two medians of a triangle ABC be equal, then it is an isosceles triangle.
Solution
Let BE and CF be two medians of ∆ABC.
Take A an origin. Let
Since E is mid-point of AC
position vector of E is 
Similarly position vector of F is
.
Now,
and
From given condition,
Take A an origin. Let
Since E is mid-point of AC
position vector of E is Similarly position vector of F is
.Now,
and
From given condition,
