I don't talk about the geometry of the lines up in the air.
Your photo shows a 3 phase supply system.
We need to look at the voltages only: in a 220 kV system we have
pahse A : u(t) = sqrt(2)*220000 * sin ( 2* pi*50 *t )
pahse B : u(t) = sqrt(2)*220000 * sin ( 2* pi*50 *t + 120 degrees)
pahse C : u(t) = sqrt(2)*220000 * sin ( 2* pi*50 *t + 240 degrees)
These phase offsets do have a prominent influence on the far field E vector.(a distance large in comparison to the distance between the lines - this is where geometry really counts)
Likewise for the current under your assumption of purely resistive load.
I think you do it right only the text was misleading to me.