I am trying to understand Kirchhoff's voltage law in reference to AC circuits and this is a dummy problem I have solved to show my doubt.Quoting my textbook, voltages across components in a LCR circuit are phasors so they are not added algebraically but vectorially, going by the statement I could not verify the asserted statement, here in my problem voltages being added algebraically give correct result but not so when vector addition is involved, please correct my reasoning.
The notation used is very generic, shouldn't be a problem.