Question

$\overrightarrow{A}$ is a vector which when added to the resultant of vectors $(2\hat{i}-3\hat{j}+4\hat{k})$ and $(\hat{i}+5\hat{j}+2\hat{k})$ yields a unit vector along the y-axis. Then vector $\overrightarrow{A}$ is

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

Answer 1

The correct option is A

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

As per the question, $\overrightarrow{A}+(2\hat{i}-3\hat{j}+4\hat{k})+(\hat{i}+5\hat{j}+2\hat{k})=\hat{j}$
$\Rightarrow \overrightarrow{A}+3\hat{i}+2\hat{j}+6\hat{k}=\hat{j}$
$\Rightarrow \overrightarrow{A}=-3\hat{i}-\hat{j}-6\hat{k}$
Hence, the correct option is (a).