Question

The unit vector parallel to the resultant of the vectors $\overrightarrow{A}=4\hat{i}+3\hat{j}+6\hat{k}$ and $\overrightarrow{B}=-\hat{i}+3\hat{j}-8\hat{k}$ is

• A. $\frac{1}{49}(3\hat{i}+6\hat{j}-2\hat{k})$
• B. $\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})$
• C. $\frac{1}{7}(3\hat{i}+6\hat{j}+2\hat{k})$
• D. $\frac{1}{49}(3\hat{i}-6\hat{j}+2\hat{k})$

Answer 1

The correct option is B $\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})$

Resultant of vectors $\overrightarrow{A}$ and $\overrightarrow{A}$
$\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}$
$=4\hat{i}+3\hat{j}+6\hat{k}\hat{i}+3\hat{j}-8\hat{k}$
$\overrightarrow{R}=3\hat{i}+6\hat{j}-2\hat{k}$
$\hat{R}=\frac{\overrightarrow{R}}{|\overrightarrow{R}|}$

$=\frac{3\hat{i}+6\hat{j}-2\hat{k}}{\sqrt{3^2+6^3+(-2{)}^2}}$
$=\frac{3\hat{i}+6\hat{j}-2\hat{k}}{7}$

Final answer (a)