Question

If the position vectors of $A,B,C$ are $3\hat{i}+\hat{j}-\hat{k}$, $\hat{i}-2\hat{j}$, $2\hat{i}-\hat{j}+3\hat{k}$ then the position vector of the centroid of the triangle $ABC$ is

• A. $2\hat{i}+\frac{-2}{3}\hat{j}+\frac{2}{3}\hat{k}$
• B. $2\hat{i}+\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}$
  
• C. $3\hat{i}+\frac{2}{3}\hat{j}+\frac{4}{3}\hat{k}$
• D. None of these

Answer 1

The correct option is A $2\hat{i}+\frac{-2}{3}\hat{j}+\frac{2}{3}\hat{k}$

Centroid of a triangle is given by

$G=\frac{\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}}{3}$
Putting the given values we get

$=\frac{3\hat{i}+\hat{j}-\hat{k}+\hat{i}-2\hat{j}+2\hat{i}-\hat{j}+3\hat{k}}{3}$
$=2\hat{i}+\frac{-2}{3}\hat{j}+\frac{2}{3}\hat{k}$