Question

The vector that must be added to the vector $\hat{i}-3\hat{j}+2\hat{k}$ and $3\hat{i}+6\hat{j}-7\hat{k}$ so that the resultant vector is a unit vector along the y­­-axis is

• A. $4\hat{i}+2\hat{j}+5\hat{k}$
  
• B. $-4\hat{i}-2\hat{j}+5\hat{k}$
• C. $3\hat{i}+4\hat{j}+5\hat{k}$
  
• D. $Nullvector$

Answer 1

The correct option is B $-4\hat{i}-2\hat{j}+5\hat{k}$

Unit vector along y axis = $\hat{j}$ so the required vector
$=\hat{j}-\left[\right(\hat{i}-3\hat{j}+2\hat{k})+(3\hat{i}+6\hat{j}-7\hat{k}\left)\right]=-4\hat{i}-2\hat{j}+5\hat{k}$