Question

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

• A. $3$
• B. $2$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $3$

$\overrightarrow{p}=\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$ as per the orthocentre definition.
Also, centroid $\overrightarrow{g}=\frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{3}$ where, $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are the position vectors of points $A,B,C$ of the triangle respectively.