Question

Unit vector parallel to the resultant of vectors $\overrightarrow{A}=4\hat{i}-3\hat{j}$ and $\overrightarrow{B}=8\hat{i}+8\hat{j}$

• A. $\frac{24\hat{i}+5\hat{j}}{13}$
• B. $\frac{12\hat{i}+5\hat{j}}{13}$
• C. $\frac{6\hat{i}+5\hat{j}}{13}$
• D. $Noneofthese$

Answer 1

The correct option is B

$\frac{12\hat{i}+5\hat{j}}{13}$

Resultant of vectors $\overrightarrow{A}$ and $\overrightarrow{B}$
$\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}=4\hat{i}-3\hat{j}+8\hat{i}+8\hat{j}=12\hat{i}+5\hat{j}$
$\hat{R}=\frac{\overrightarrow{R}}{|R|}=\frac{12\hat{i}+5\hat{j}}{\sqrt{(12{)}^2+(5{)}^2}}=\frac{12\hat{i}+5\hat{j}}{13}$