Find the unit vector in xy-plane, making an angle 60^º with the positive direction of x-axis.

(1/2)\(\hat{i}\) +(√(3)/2)\(\hat{j}\) 

Let   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 x-axis.

Therefore, for θ= 60^º

 \(\vec{r}\)= (cos60^º)\(\hat{i}\)  +(sin60^º)\(\hat{j}\) 

Hence the required unit vector  \(\vec{r}\) = (1/2)\(\hat{i}\) +(√(3)/2)\(\hat{j}\)