Question

Let $A=2\hat{i}+4\hat{j}-\hat{k}$, $B=4\hat{i}+5\hat{j}+\hat{k}$. If the centroid $G$ of the triangle $ABC$ is $3\hat{i}+5\hat{j}-\hat{k}$, then the position vector of $C$ is

• A. $3\hat{i}-6\hat{j}+3\hat{k}$
• B. $3\hat{i}-6\hat{j}-3\hat{k}$
• C. $3\hat{i}-6\hat{j}+2\hat{k}$
• D. $3\hat{i}+6\hat{j}-3\hat{k}$

Answer 1

Answer: (D)

$3\hat{i}+6\hat{j}-3\hat{k}$

Centroid is given by

$G=\frac{\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}}{3}$

Putting given values to find $\overrightarrow{C}$
$\Rightarrow 3(3\hat{i}+5\hat{j}-k)=2\hat{i}+4\hat{j}-\hat{k}+4\hat{i}+5\hat{j}+\hat{k}+\overrightarrow{C}$
$\Rightarrow 3\hat{i}+6\hat{j}-3\hat{k}=\overrightarrow{C}$