1. Okay, so I am gonna prove that [tex]\int H_a\cdot H_bdv=0[/tex] Hint: Use vector Identities H is the Magnetic Field and v is the volume. 2. Relevant equations this this [tex]k_bH_b=\nabla \times E_b[/tex] [tex]k_aH_a=\nabla \times E_a[/tex] k is the wave vector and E is the electric field 3. The attempt at a solution It is known that H_a and H_b are really perpendicular to each other, so their dot product is just simple, zero. Well I am dead wrong! I got only 2 points out of 10, so its definitely not the solution for proving it. Its now semester break, so I could not ask our professor the solution (no classes now), plus he is too busy. But I am still itching to find the correct solution for this. The hint tells to use vector identities, how could I figure It out?