⚠️ Inline KaTeX/MathJax $...$ inside [grid] can leak BBCode when used with [details]

i thought i should at least conculde mathematically accurate information, not ChatGPT waffle :grinning_face:


\frac{1}{r^2 \sin\theta} \left| \begin{matrix} \textcolor{orange}{\hat{r}} & r\hat{\theta} & r\sin\theta\,\hat{\phi} \\ \partial_r & \boxed{\partial_\theta} & \boxed{\partial_\phi} \\ A_r & \boxed{r A_\theta} & \boxed{r\sin\theta\, A_\phi} \end{matrix} \right|
\frac{1}{r^2 \sin\theta} \left| \begin{matrix} \textcolor{orange}{\hat{r}} & r\hat{\theta} & r\sin\theta\,\hat{\phi} \\ \partial_r & \boxed{\partial_\theta} & \boxed{\partial_\phi} \\ A_r & \boxed{r A_\theta} & \boxed{r\sin\theta\, A_\phi} \end{matrix} \right|
the 1st term of the Curl

[center]
\Huge \frac{1}{r^2 \sin\theta} \cdot \textcolor{orange}{\hat{r}}\begin{vmatrix} \partial_\theta & \partial_\phi \\ r A_\theta & r\sin\theta\, A_\phi \end{vmatrix}
[/center]


\textcolor{red}{ \frac{1}{r^2 \sin\theta} \left| \begin{matrix} \hat{r} & \textcolor{purple}{r\hat{\theta}} & r\sin\theta\,\hat{\phi} \\ \left.\overrightarrow{\partial_r}\right| & \partial_\theta & \left|\overrightarrow{\;\;\;\;\;\partial_\phi\;\;\;\;\;\;}\right. \\ \left.\underrightarrow{A_r}\right| & r A_\theta & \underrightarrow{\biggl| \, r\sin\theta\, A_\phi \,} \end{matrix} \right| }
\textcolor{green}{ \frac{1}{r^2 \sin\theta} \left| \begin{matrix} \hat{r} & \textcolor{purple}{r\hat{\theta}} & r\sin\theta\,\hat{\phi} \\ \left|\overrightarrow{\partial_r}\right. & \partial_\theta & \left.\overrightarrow{\;\;\;\;\;\partial_\phi\;\;\;\;\;\;}\right| \\ \left|\underrightarrow{A_r}\right. & r A_\theta & \underrightarrow{ \, r\sin\theta\, A_\phi \, \biggl|} \end{matrix} \right| }
the 2nd term of the Curl

[center]
\Huge \textcolor{red}{- \frac{1}{r^2 \sin\theta} \cdot \textcolor{purple}{r\hat{\theta}}\begin{vmatrix} \partial_\phi & \partial_r \\ r\sin\theta\, A_\phi & A_r \end{vmatrix} }

\Huge \textcolor{green}{+ \frac{1}{r^2 \sin\theta} \cdot \textcolor{purple}{r\hat{\theta}}\begin{vmatrix} \partial_r & \partial_\phi \\ A_r & r\sin\theta\, A_\phi \end{vmatrix} }
[/center]


\frac{1}{r^2 \sin\theta} \left| \begin{matrix} \hat{r} & r\hat{\theta} & \textcolor{blue}{r\sin\theta\,\hat{\phi}} \\ \boxed{\partial_r} & \boxed{\partial_\theta} & \partial_\phi \\ \boxed{A_r} & \boxed{r A_\theta} & r\sin\theta\, A_\phi \end{matrix} \right|
\frac{1}{r^2 \sin\theta} \left| \begin{matrix} \hat{r} & r\hat{\theta} & \textcolor{blue}{r\sin\theta\,\hat{\phi}} \\ \boxed{\partial_r} & \boxed{\partial_\theta} & \partial_\phi \\ \boxed{A_r} & \boxed{r A_\theta} & r\sin\theta\, A_\phi \end{matrix} \right|
the 3rd term of the Curl

[center]
\Huge \frac{1}{r^2 \sin\theta} \cdot \textcolor{blue}{r\sin\theta\,\hat{\phi}}\begin{vmatrix} \partial_r & \partial_\theta \\ A_r & r A_\theta \end{vmatrix}
[/center]


i have created another Topic about colouring the text in the details panes titles’ , which could match the 3 colours on specific elements