For vector $\vec{E}, \vec{H}$
(a) $ \iint_{S} (\vec{E}\times\vec{H})\cdot d\vec{s} = 0 $ (The integral here is closed integral but i cannot use \oiint here)
then what can i know about vectors $\vec{E}, \vec{H} $?
I thought about $ d\vec{s} = \hat{n} ds $
$ (\vec{E}\times\vec{H})\cdot \hat{n} = \hat{n} \cdot (\vec{E}\times\vec{H}) = \vec{E}\cdot(\vec{H}\times\hat{n}) = \vec{H} \cdot (\hat{n}\times\vec{E})$
Then, If
(1) $\hat{n}\times\vec{E}=0$ on surface $S$
or (2) $\hat{n}\times\vec{H}=0$ on surface $S$
or (3) $\hat{n}\times\vec{E}=0$ on a portion of $S$ and $\hat{n}\times\vec{H}=0$ on the rest of $S$
is satisfied, $ \iint_{S} (\vec{E}\times\vec{H})\cdot d\vec{s} = 0 $
Ie, if (1) or (2) or (3) is satisfied, (a) is correct. But I don't know that if (a) is correct, whether (1) or (2) or (3) is the only possible cases or not. How do you think??