Question

Let $\stackrel{\rightharpoonup }{p}$ is the p.v. of the orthocentre &$\stackrel{\rightharpoonup }{g}$ is the p.v. of the centroid of the triangle ABC, where circumcentre is the origin. If $\stackrel{\rightharpoonup }{p}=K\stackrel{\rightharpoonup }{g}$, then $K=$

• A. 3
• B. 2
• C. 1/3
• D. 2/3

Answer 1

Answer: (A)

3

Let $O$ be a fixed origin then position sector of $P$ is

Centroid is intersection is

$\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}$

orthocentre intersection of altitudes So that in a triangle $ABC$ the orthocentre $H$, centroid $G$ and circumcentre $M$ are collinaer and $G$ divides $HM$ internally in the ratio $2:1$

$\therefore g=\frac{2\times m+HP}{3}\Rightarrow p=3g$

$K=3$ $(m=0,0,0)$