Antenna Partial Directivity and Gain

Hello,

I am a bit confused about the notion of partial directivity and gain.

According to textbooks and papers the total directivity is defined as the sum of the partial directivities (the same for gain).

But the common practice to get the sum of two orthogonal vectors is to take the vector sum. i.e. Instead of G = G_phi + G_theta, shouldn't it be G = sqrt(G_theta^2 + G_phi^2)?

Can someone clarify this? Or is it just that the antenna community decided to adopt this definition? If yes, is there a intuition based reasoning for this?

Thanks.

I think you have a small confusion between fields and power densities.

Therefore,

And,

Hope this solved your doubt.