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=\frac1{(3\cos\theta+2\sin\theta)\sin\varphi+3\cos\varphi}`