Question

What vector must be added to the two vectors $\hat{i}-2\hat{j}+2\hat{k}and2\hat{i}+\hat{j}-\hat{k},$ so that the resultant may be a unit vector along x-axis

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

Answer 1

The correct option is B

$-2\hat{i}+\overrightarrow{j}-\overrightarrow{k}$

$(\hat{i}-2\hat{j}+2\hat{k})+(2\hat{i}+\hat{j}-\hat{k})+\overrightarrow{R}=i$
$\therefore$ Required vector $\overrightarrow{R}=-2\hat{i}+\overrightarrow{j}-\overrightarrow{k}$