Question

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

Answer 1

If $\overrightarrow{r}$ is a unit vector in the XY-plane, then $\overrightarrow{r}=\cos \theta \hat{i}+\sin \theta \hat{j}$.

Here, $\theta$ is the angle made by the unit vector with the positive direction of the x-axis.

Therefore, for $\theta ={30}^o$

$\overrightarrow{r}=\cos {30}^o\hat{i}+\sin {30}^o\hat{j}$

$\overrightarrow{r}=\frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j}$.