Question

If $\overrightarrow{A}=2\overrightarrow{i}-\hat{j}+3\hat{k}$ & $\overrightarrow{B}=3\hat{i}-2\hat{j}+2\hat{k}$. Find the unit vector of $(\overrightarrow{A}+\overrightarrow{B})$

Answer 1

Given that,

The vectors is

$\overrightarrow{A}=2\hat{i}-\hat{j}+3\hat{k}$

$\overrightarrow{B}=3\hat{i}-2\hat{j}+2\hat{k}$

Now, the unit vector of $\overrightarrow{A}+\overrightarrow{B}$

$\frac{\overrightarrow{A}+\overrightarrow{B}}{|A+B|}=\frac{(2\hat{i}-\hat{j}+3\hat{k})+(3\hat{i}-2\hat{j}+2\hat{k})}{|A+B|}$

$\frac{\overrightarrow{A}+\overrightarrow{B}}{|A+B|}=\frac{5\hat{i}-3\hat{j}+5\hat{k}}{\sqrt{25+9+25}}$

$\frac{\overrightarrow{A}+\overrightarrow{B}}{|A+B|}=\frac{5}{\sqrt{59}}\hat{i}-\frac{3}{\sqrt{59}}\hat{j}+\frac{5}{\sqrt{59}}\hat{k}$

Hence, the unit vector of $\overrightarrow{A}+\overrightarrow{B}$ is $\frac{5}{\sqrt{59}}\hat{i}-\frac{3}{\sqrt{59}}\hat{j}+\frac{5}{\sqrt{59}}\hat{k}$