Question

Let $\overrightarrow{p}$ be the position vector of the orthocenter and $\overrightarrow{g}$ be the position vector of the centroid of the triangle ABC, whese circumcenter is the origin. If $\overrightarrow{p}=K\overrightarrow{g}$, then K=

• A. 3
• B. 2
• C. 1/3
• D. 2/3

Answer 1

Answer: (A)

3

Position vector of P is $\overrightarrow{OP}$

Centroid intersection is $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

In triangle ABC the orthocentre H, centroid G and circumcenter m are colinear & G divides HM internally in the ratio $2:1$

$g=\frac{2M+1\times P}{3}$

but $M=(0,0,0)$

$P=3y$

$k=3$.