Question

If a displacement vector of $AB$ is $\hat{i}+\hat{j}+2\hat{k}$ and point $A$ having a position vector $2\hat{i}+5\hat{j}+6\hat{k}$, then find the position vector of $B$ ?

• A. $3\hat{i}+\hat{j}+3\hat{k}$
• B. $3\hat{i}+\hat{j}+2\hat{k}$
• C. $3\hat{i}+\hat{j}+4\hat{k}$
• D. $\hat{i}+4\hat{j}+4\hat{k}$

Answer 1

The correct option is D $\hat{i}+4\hat{j}+4\hat{k}$

Given, $\overrightarrow{AB}=\hat{i}+\hat{j}+2\hat{k}$
$\overrightarrow{B}=?$
$\overrightarrow{A}=2\hat{i}+5\hat{j}+6\hat{k}$

displacement vector :
$\overrightarrow{AB}=\overrightarrow{A}-\overrightarrow{B}$
$\Rightarrow \overrightarrow{B}=\overrightarrow{A}-\overrightarrow{AB}$
$\Rightarrow \overrightarrow{B}=(2-1)\hat{i}+(5-1)\hat{j}+(6-2)\hat{k}$
$\Rightarrow \overrightarrow{B}=\hat{i}+4\hat{j}+4\hat{k}$