Bob,
You have me very confused here.
You keep saying that vector addition is necessary.
You keep quoting me and saying that I can't use simple addition.
But I _am_ using vector addition. I _said_ that 1560 VA is being delivered by leg A to the example load, and that 1560VA is being delivered by leg B, yet only 2704W is being delivered to the load. That answer comes from doing the vector analysis of the situation. The whole concept of volt amperes being different from watts is deeply rooted in the vector approximation of AC circuits.
The whole point of saying "2x1560VA being supplied by the transformer, yet only 2704W being delivered to the load" is an explicit example that phase angle differences are present in this system and must be accounted for using vector math. Clearly, 13A is flowing through leg A transformer coil, and 13A is flowing through the leg B transformer coil. Thus the heating experienced by the _transformer_ is what one would expect from having 1560VA per phase supplied by that transformer. But the power being delivered to the load is only 2704W, and the _difference_ between 3120VA and 2704W is explicitly caused by phase angle differences.
One must with the _voltages_ supplied by the leg A and leg B transformer coils. To determine the composite voltage from leg A to leg B you must use vectors (or some other analysis technique that accounts for the phase difference). The voltage between legs A and B is a vector quantity. Once you've calculated the voltage from leg A to leg B you can calculate the current flowing through the load.
Do the math yourself.
Define the leg A to neutral voltage as your phase zero current.
The leg B to neutral voltage is at phase angle 120 degrees.
Now calculate the phase angle of the leg A to leg B voltage. It is neither 0 nor 120 degrees.
The current through the resistive load will be in phase with the leg A to leg B voltage calculated above.
This means that the current in the leg A transformer coil is _not_ in phase with the voltage across the leg A transformer coil.
-Jon
