Thomas' Calculus 13th Edition

$r(u,v)=xi+3 \cos u \space j+3 \sin v \space k; \\ 0 \le u \le 3$ and $0 \le v \le 2\pi$
Use spherical coordinates as: $x= P \sin \phi \cos \theta; y=Pl \sin \phi \sin \theta; z=Pl \cos \phi$ $0 \le \phi \le \pi; \\0 \le \theta \le 2 \pi$ We know that $r(r, \theta)=xi+yj+zk$ or, $r^2=x^2+y^2+z^2$ We have $y^2+z^2=9$ Now, $r(u,v)=xi+(3 \cos u)j+(3 \sin v)k$; and $y^2+z^2=9 ;\\ 0 \le u \le 3 \space$ and $\space 0 \le v \le 2\pi$ Hence: $r(u,v)=xi+3 \cos u \space j+3 \sin v \space k; \\ 0 \le u \le 3$ and $0 \le v \le 2\pi$