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

Question:

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

Solution:

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

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

Therefore, for θ = 30°:

$\vec{r}=\cos 30^{\circ} \hat{i}+\sin 30^{\circ} \hat{j}=\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}$

Hence, the required unit vector is $\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}$.