# RMS values and phasor diagrams

In RL circuits (AC source) we use vectors to calculate the total voltage, I understand that we cannot add them algebraically because they do not exist at the same time as we are using rms values for both voltages which represent the peak of each wave (multiplied by $$0.707$$); I understand the phase shift between the two.

My question is:

Why do we apply vector rules to calculate the peak(or rms value) of the total voltage wave whereas we use different peaks of another two waves?

I mean how could the phasor diagram represent the shift angle and, at the same time, calculate the value of the total voltages ?

   I Z cos(wt+ϕ) = I Xc cos(wt – π/2) + I R cos(wt) + I XL cos(wt + π/2)