A displacement vector $\overrightarrow{r}$ in the xy-plane is 12m long and directed at angle $\theta ={30}^o$ with x-axis

As the vector is in xy plane the z-component is zero.

$\overrightarrow{r}=r\cos \theta \overrightarrow{i}+r\sin \theta \overrightarrow{j}$

Given that the magnitude is 12m

$\Rightarrow r\cos \theta =12\cos {30}^o=12\times \frac{\sqrt{3}}{2}=6\sqrt{3}m$

$r\sin \theta =12\sin {30}^o=12\times \frac{1}{2}=6m$