Question

Let $P$ be a point interior to the acute triangle $A B C$. If $\overrightarrow{P A}+\overrightarrow{P B}+\overrightarrow{P C}$ is a null vector, then w.r.t. triangle $A B C$ point $P$ is its

• A. centroid
• B. orthocentre
• C. incentre
• D. circumcentre

Answer 1

Answer: (A)

$\vec{a}-\vec{p}+\vec{b}-\vec{p}+\vec{c}-\vec{p}=0$
or $ \vec{p}=\frac{\vec{a}+\vec{b}+\vec{c}}{3}$
Hence, $P$ is centroid.