Question

If $\overrightarrow{A}$ = 3 $\hat{i}$ + 4 $\hat{j}$, then what is unit vector along $\overrightarrow{A}$ ?

• A. $\frac{3}{5}\hat{i}$ + $\frac{4}{5}\hat{j}$
• B. $\frac{4}{5}\hat{i}$ + $\frac{3}{5}\hat{j}$
• C. $\frac{5}{4}\hat{i}$ + $\frac{5}{3}\hat{j}$
• D. $\frac{5}{3}\hat{i}$ + $\frac{5}{4}\hat{j}$

Answer 1

The correct option is A $\frac{3}{5}\hat{i}$ + $\frac{4}{5}\hat{j}$

According to the definition,
Unit vector along $\overrightarrow{A}$, $\left(\hat{A}\right)$ = $\frac{\overrightarrow{A}}{|\overrightarrow{A}|}$

Now magnitude of $\overrightarrow{A}$
= $\sqrt{(3{)}^2+(4{)}^2}=5.$

Hence, we have
$\hat{A}$ $=\frac{\overrightarrow{A}}{5}$
$=\frac{3\hat{i}+4\hat{j}}{5}$
$=\frac{3}{5}\hat{i}$ + $\frac{4}{5}\hat{j}$