Question

A unit vector parallel to the resultant of the vectors $\overrightarrow{A}=\hat{i}+4\hat{j}-2\hat{k}$ and $\overrightarrow{B}=3\hat{i}-5\hat{j}+\hat{k}$ is

• A. $4\hat{i}-\hat{j}-\hat{k}$
• B. $\frac{4\hat{i}}{\sqrt{18}}-\frac{\hat{j}}{\sqrt{18}}-\frac{\hat{i}}{\sqrt{18}}$
• C. $-\frac{4\hat{i}}{\sqrt{18}}+\frac{\hat{j}}{\sqrt{18}}+\frac{\hat{k}}{\sqrt{18}}$
• D. $-4\hat{i}+\hat{j}+\hat{k}$

Answer 1

The correct option is B $\frac{4\hat{i}}{\sqrt{18}}-\frac{\hat{j}}{\sqrt{18}}-\frac{\hat{i}}{\sqrt{18}}$

Resultant, $\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}$
$\overrightarrow{R}=(\hat{i}+4\hat{j}-2\hat{k})+(3\hat{i}-5\hat{j}+\hat{k})$
$\overrightarrow{R}=4\hat{i}-\hat{j}-\hat{k}$
Unit vector along $\overrightarrow{R}$,
$\hat{R}=\frac{\overrightarrow{R}}{|\overrightarrow{R}|}$
$\hat{R}=\frac{4\hat{i}-\hat{j}-\hat{k}}{\sqrt{4^2+1^2+1^2}}$
$\hat{R}=\frac{4\hat{i}}{\sqrt{18}}-\frac{\hat{j}}{\sqrt{18}}-\frac{\hat{k}}{\sqrt{18}}$