Question

Write the equation in spherical coordinates. 3x + 2y + 3z = 1

Answer 1

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\cos\varphi\end{cases}$

$3x+2y+3z=1$
$\implies3\rho\cos\theta\sin\varphi+2\rho\sin\theta\sin\varphi+3\rho\cos\varphi=1$
$\implies\rho=\dfrac1{(3\cos\theta+2\sin\theta)\sin\varphi+3\cos\varphi}$