Question

A unit vector in the direction of resultant vector of
$\overrightarrow{A}$ = -2$\hat{i}$+3$\hat{j}$+$\hat{k}$ and $\overrightarrow{B}$ = $\hat{i}$+2$\hat{j}$-4$\hat{k}$ is

• A. -2$\hat{i}$+3$\hat{j}$+$\hat{k}$/$\sqrt{35}$
• B. $\hat{i}$+2$\hat{j}$-4$\hat{k}$/$\sqrt{35}$
• C. -$\hat{i}$+5$\hat{j}$-3$\hat{k}$/ $\sqrt{35}$
• D. -3$\hat{i}$ +$\hat{j}$+5$\hat{k}$ /$\sqrt{35}$

Answer 1

Answer: (C)

-$\hat{i}$+5$\hat{j}$-3$\hat{k}$/ $\sqrt{35}$

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

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

The resultant vector of $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\overrightarrow{R}$ = $\overrightarrow{A}$ + $\overrightarrow{B}$

$\therefore \overrightarrow{R}=(-2\hat{i}+3\hat{j}+\hat{k})+(\hat{i}+2\hat{j}-4\hat{k})=-\hat{i}+5\hat{j}-3\hat{k}$

$\overrightarrow{R}$ = $\sqrt{(-1{)}^2+(5{)}^2+(-3{)}^2}=\sqrt{1+25+9}=\sqrt{35}$

Unit vector in the direction of resultant vector of $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\overrightarrow{R}$ =$\overrightarrow{R}/|\overrightarrow{R}|$= $\frac{-\hat{i}+5\hat{j}-3\hat{k}}{\sqrt{35}}$