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

Let, $B=(2\hat{i}-3\hat{j}+4\hat{k})$ and $C=(\hat{i}+5\hat{j}+2\hat{k})$
As per the question given:
$A+B+C=1\hat{j}$
$\therefore A+(2\hat{i}-3\hat{j}+4\hat{k})+(\hat{i}+5\hat{j}+2\hat{k})=1\hat{j}$
$\therefore A=-3\hat{i}-\hat{j}-6\hat{k}$