How to show that voltages on diagram are 120° apart?
A slightly off-beat approach:



Figure 1. Intersection of the curves.

Because they're sinewaves we can use some trig functions.


At (1) the blue phase is at 0. Let's call this 0&deg;.
At (2) the blue phase is at 2400. That will be 90&deg;.
At (3) and (4), the intersection point with the other phases, the voltage is 1200 which is half the peak. We know that \$ sin\ a = 0.5 \$ has two solutions: 30&deg; and 150&deg; and that these are 120&deg; apart.