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

The Correct Option is 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 $\hat{R}=\frac{\vec{R}}{\left|\vec{R}\right|}$ $=\frac{-\hat{i}+5\hat{j}-3\hat{k}}{\sqrt{35}}$