[tex]\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\cos\varphi\end{cases}[/tex]
[tex]3x+2y+3z=1[/tex]
[tex]\implies3\rho\cos\theta\sin\varphi+2\rho\sin\theta\sin\varphi+3\rho\cos\varphi=1[/tex]
[tex]\implies\rho=\dfrac1{(3\cos\theta+2\sin\theta)\sin\varphi+3\cos\varphi}[/tex]
