Question

Let $a=\hat{i}+2\hat{j}+3\hat{k}$ and $b=3\hat{i}+\hat{j}$. Find the unit vector in the direction of the $a+b$.

• A. $\frac{4\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{34}}$
• B. $\frac{4\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{44}}$
• C. $\frac{5\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{34}}$
• D. None of these

Answer 1

The correct option is A $\frac{4\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{34}}$

Given, $a=\hat{i}+2\hat{j}+3\hat{k}$ and $b=3\hat{i}+\hat{j}$

$a+b=\left(\hat{i}+2\hat{j}+3\hat{k}\right)+\left(3\hat{i}+\hat{j}\right)$

$=4\hat{i}+3\hat{j}+3\hat{k}$

$\left|a+b\right|=\sqrt{{\left(4\right)}^2+{\left(3\right)}^2+{\left(3\right)}^2}$

$=\sqrt{16+9+9}$

$=\sqrt{34}$

So, unit vector in the direction of $a+b$

$=\frac{a+b}{\left|a+b\right|}$

$=\frac{4\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{34}}$