If O and O’ are circumcentre and orthocentre of Δ ABC, then vector (OA) + vector(OB) + vector(OC) equals A. 2vectoro o'

Question

If O and O’ are circumcentre and orthocentre of Δ ABC, then \(\vec{OA}+\vec{OB}+\vec{OC}\)  equals

A. \(2\vec OO'\)

B. \(O\vec {O'}\)

C. \(2\vec {O'}O\)

D. \(2\vec {O'}O\)

Answer 1

Correct option is  B. \(O\vec {O'}\) 

Let the vertices of the triangle ABC be A ( \(\vec a\)), B ( \(\vec b\)) & C ( \(\vec c\)), with respect to the origin.

O (x, y) is the circumcentre & O’ (0, 0) is the orthocenter.

As the centroid ‘G’ divides the orthocentre ‘C’ (x ,y) and circumcentre (0, 0) in the ratio 2 : 1. By using Section Formula,