The expression that is given is:
[tex]\int_{A \infty} e_j \times h_k* \cdot \widehat{z} dA = 0 [/tex]

where * denotes the complex conjugate, and z^ is the unit vector in the direction of propagation (along the axis of the fibre).

Can anyone explain why this mathematical expression indicates orthogonality? I am trying to interpret the mathematics rather than just accept it.

What I've done:
I tried to explain it by saying that the dot product between two perpendicular vectors will be 0. But in this sense, I only see the indication that a component perpendicular to both e and h (cross product) is perpendicular to the direction of propagation.