Question

A unit vector parallel to the resultant of the vectors

$\overrightarrow{A}=4\hat{i}+3\hat{j}+6\hat{k}$ and $\overrightarrow{B}=-\hat{i}+8\hat{j}-8\hat{k}$

• A. $\frac{3\hat{i}+11\hat{j}-2\hat{k}}{2}$
• B. $\frac{\hat{i}+2\hat{j}-3\hat{k}}{\sqrt{166}}$
• C. $\frac{3\hat{i}+11\hat{j}-2\hat{k}}{\sqrt{134}}$
• D. $\frac{4\hat{i}+6\hat{j}+8\hat{k}}{\sqrt{11}}$

Answer 1

Answer: (C)

Resultant of vectors $\overrightarrow{A}$ and $\overrightarrow{B}$
So, $\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}$
$\overrightarrow{R}=4\hat{i}+3\hat{j}+6\hat{k}-\hat{i}+8\hat{j}-8\hat{k}$
$\overrightarrow{R}=3\hat{i}+11\hat{j}-2\hat{k}$
$\vec{R}=\frac{3\hat{i}+11\hat{j}-2\hat{k}}{\sqrt{(3{)}^2+(11{)}^2+(-2{)}^2}}$
$\vec{R}=\frac{3\hat{i}+11\hat{j}-2\hat{k}}{\sqrt{9+121+4}}=\frac{3\hat{i}+11\hat{j}-2\hat{k}}{\sqrt{134}}$