Answer
$r(u,v)=\lt \sqrt 3 \sin u \cos v,\sqrt 3 \sin u \sin v, \sqrt 3 \cos u \gt$; $\dfrac{\pi}{3} \le u \le \dfrac{2\pi}{3}$ and $0 \le v \le 2 \pi$
Work Step by Step
The spherical coordinates are: $x= l \sin \phi \cos \theta, y= l \sin \phi \sin \theta, z= l \cos \phi $ ; $0 \le \phi \le \pi$ and $0 \le \theta \le 2 \pi$
Here, we have $x^2+y^2+z^2 =3$
$x= \sqrt 3 \sin u \cos v, y= \sqrt 3 \sin u \sin v, z= \sqrt 3 \cos u $ ;
Thus,
$r(u,v)=\lt \sqrt 3 \sin u \cos v,\sqrt 3 \sin u \sin v, \sqrt 3 \cos u \gt$; $\dfrac{\pi}{3} \le u \le \dfrac{2\pi}{3}$ and $0 \le v \le 2 \pi$
