Question

If P is orthocenter, Q is circumcenter and G is centroid of a triangle ABC, then prove that vector QP = 3QG

Answer 1

Let \(\overline{p}\) and \(\overline{g}\) be the position vectors of P and G w.r.t. the circumcentre Q.

i.e. \(\overline{QP} = p\) and \(\overline{QG} = g.\)

We know that Q, G, P are collinear and G divides segment QP internally in the ratio 1 : 2 

∴ by section formula for internal division,