Question

Write down a unit vector in $XY$-plane, making an angle of $30°$ with the positive direction of the x-axis.

• A. $\frac{\sqrt{3}}{2}i+\frac{1}{2}j$
• B. $i+j$
• C. $i$
• D. $j$

Answer 1

The correct option is A

$\frac{\sqrt{3}}{2}i+\frac{1}{2}j$

Explanation for the correct option:

Finding unit vector in $XY$-plane

The angle made by the unit vector with the X-axis$=30°$

If $\overrightarrow{r}$is the unit vector in the $XY$ plane, $\overrightarrow{r}=i\cos \theta +j\sin \theta$ where, $\theta$ is the angle made by the vector with the x-axis.

Substituting the value of $\theta$,

$\overrightarrow{r}=\left(\cos 30°\right)i+\left(\sin 30°\right)j$

$\Rightarrow \overrightarrow{r}=\frac{\sqrt{3}}{2}i+\frac{1}{2}j\left(\because \cos 30°=\frac{\sqrt{3}}{2},\sin \theta =\frac{1}{2}\right)$

Hence the correct option is A.