Question

The vectors 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 $-4\hat{i}-2\hat{j}+5\hat{k}$

Given that

Vector

$\overrightarrow{A}=\hat{i}-3\hat{j}+2\hat{k}$

$\overrightarrow{B}=3\hat{i}+6\hat{j}-7\hat{k}$

$\overrightarrow{R}=x\hat{i}+y\hat{j}+z\hat{k}$

Now, $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{R}=\hat{j}$

Now, put the value

$\hat{i}-3\hat{j}+2\hat{k}+3\hat{i}+6\hat{j}-7\hat{k}+x\hat{i}+y\hat{j}+z\hat{k}=0\hat{i}+1\hat{j}+0\hat{k}$

$4+x=0$

$x=-4$

$3+y=1$

$y=-2$

$-5+z=0$

$z=5$

So, the vector is

$\overrightarrow{R}=-4\hat{i}-2\hat{j}+5\hat{k}$

Hence, the resultant vector is $-4\hat{i}-2\hat{j}+5\hat{k}$