Does orthogonal beamforming mean $\mathbf f_a \cdot \mathbf f_b =0$?
Orthogonality might be considered in literature as background knowledge. The definition is somehow a converse version. If $\cdot $ denotes an inner product (or a dot or scalar product), and whenever 
 $\mathbf  f_a \cdot \mathbf f_b = 0$, then $f_a$ and  $f_b$ are said to be orthogonal.

Note that, if $\mathbf  f_a$ is zero, it is orthogonal to everything.