Question

ques

Answer 1

How do you find
\[\vec \nabla \psi \times \vec \nabla \zeta\]
In spherical coordinates??
I think it will be
\[\vec \nabla \psi \times \vec \nabla \zeta=\left|\begin{matrix}\hat e_{r} & \hat e_{\theta} & \hat e_{\varphi} \\ \frac{\partial \psi}{\partial r} & \frac{1}{r}\frac{\partial \psi}{\partial \theta}&\frac{1}{rsin(\theta)}\frac{\partial \psi}{\partial \varphi} \\ \frac{\partial \zeta}{\partial r} & \frac{1}{r}\frac{\partial \zeta}{\partial \theta} &\frac{1}{rsin(\theta)}\frac{\partial \zeta}{\partial \varphi} \end{matrix}\right|\]

@IrishBoy123

Answer 2

of the top of my head, not sure

spherical coordinates are toxic for cross and dot products