Question

A unit vector in the direction of resultant vector of $\vec{A}=-2\hat{i}+3\hat{j}+\hat{k}$ and $\vec{B}=\hat{i}+2\hat{j}-4\hat{k}$ is

• A. $\frac{-2\hat{i}+3\hat{j}+\hat{k}}{\sqrt{35}}$
• B. $\frac{\hat{i}+2\hat{j}-4\hat{k}}{\sqrt{35}}$
• C. $\frac{-\hat{i}+5\hat{j}-3\hat{k}}{\sqrt{35}}$
• D. $\frac{-3\hat{i}+\hat{j}+5\hat{k}}{\sqrt{35}}$

Answer 1

Answer: (C)

Here, $\vec{A}=-2\hat{\hat{i}}+3\hat{j}+\hat{k}$
$\vec{B}=\hat{i}+2\hat{j}-4\hat{k}$
The resultant vector of $\vec{A}$ and $\vec{B}$ is
$\vec{R}=\vec{A}+\vec{B}$
$\therefore \vec{R}=\left(-2\hat{i}+3\hat{j}+\hat{k}\right)+\left(\hat{i}+2\hat{j}-4\hat{k}\right)$
$=-\hat{i}+5\hat{j}-3\hat{k}$
$\left|\vec{R}\right|=\sqrt{{\left(-1\right)}^2+{\left(5\right)}^2+{\left(-3\right)}^2}$
$=\sqrt{1+25+9}$
$=\sqrt{35}$
Unit vector in the direction of resultant vector of $\vec{A}$ and $\vec{B}$ is
$\hat{R}=\frac{\vec{R}}{|\vec{R}|}$
$=\frac{-\hat{i}+5\hat{j}-3\hat{k}}{\sqrt{35}}$