Commercial electricity is generated and transmitted as three phase electricity. Instead of a single emf = 0 cos t, three separate wires carry

Commercial electricity is generated and transmitted as three phase electricity. Instead of a single emf Ԑ = Ԑ₀ cos ωt, three separate wires carry currents for the emfs Ԑ₁ = Ԑ₀ cos ωt, Ԑ₂ = Ԑ₀ cos(ωt + 120°), and Ԑ₃ = Ԑ₀ cos(ωt - 120°). This is why the long-distance transmission lines you see in the countryside have three parallel wires, as do many distribution lines within a city.
a. Draw a phasor diagram showing phasors for all three phases of a three-phase emf.
b. Show that the sum of the three phases is zero, producing what is referred to as neutral. In single-phase electricity, provided by the familiar 120 V/60 Hz electric outlets in your home, one side of the outlet is neutral, as established at a nearby electrical substation. The other, called the hot side, is one of the three phases. (The round opening is connected to ground.)
c. Show that the potential difference between any two of the phases has the rms value √3 Ԑ_rms, where Ԑ_rms is the familiar single-phase rms voltage. Evaluate this potential difference for Ԑ_rms = 120 V. Some high-power home appliances, especially electric clothes dryers and hot-water heaters, are designed to operate between two of the phases rather than between one phase and neutral. Heavy-duty industrial motors are designed to operate from all three phases, but full three-phase power is rare in residential or office use.