Question

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

Answer 1

If $\vec{r}$ is a unit vector in the $XY-$plane,then $\vec{r}=cosθ\hat{i}+sinθ\hat{j}.$
Here,θ is the angle made by the unit vector with the positive direction of the $x-axis.$
Therefore,for $θ=30°:$
$\vec{r}=cos30^{\degree}\hat{i}+sin30^{\degree}\hat{j}={\frac{\sqrt{3}}{2}}\hat{i}+\frac{1}{2}\hat{j}$
Hence,the required unit vector is ${\frac{\sqrt{3}}{2}}\hat{i}+\frac{1}{2}\hat{j}$.