Question
If the median of the base of a triangle is perpendicular on the base, then prove that the triangle is an isosceles.
Solution
Let ABC be a triangle in which the median AD is perpendicular to base BC.
Take A as origin. Let
be position vectors of B and C so that 
.
Since D is mid-point of BC
position vector of D is 
i.e.,
Also,
Since
Take A as origin. Let
be position vectors of B and C so that .Since D is mid-point of BC
position vector of D is i.e.,
Also,
Since
