Question

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

• 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. None of these

Answer 1

The correct option is B $\frac{12\hat{i}+5\hat{j}}{13}$

Resultant is given as:

$\overrightarrow{A}+\overrightarrow{B}=4\hat{i}-3\hat{j}+8\hat{i}+8\hat{j}=12\hat{i}+5\hat{j}$
Thus unit vector is given as: $\frac{12\hat{i}+5\hat{j}}{\sqrt{{12}^2+5^2}}$
which gives, $\frac{12\hat{i}+5\hat{j}}{13}$