A balanced three$-$phase wye$-$source with a positive sequence is powering wye loads:

Load $1$: $15$kVA with a zero$-$power factor $($lagging$)+$

Load $2$: $15$ kVA with a power factor of $0\mathrm{.}50($leading$)-$

Load $3$: $15$ kVA with a power factor of $0\mathrm{.}75($lagging$)+$

The line$-$to$-$line voltage at the load is $415\mathrm{.}7$V$\_($RMS$),$ and the line impedance is $1-$j$4\mathrm{.}2[/].$ Assume the line$-$to$-$line voltage at the load V$\_$ab has the angle of $30$

a$)$ Find the power factor at the $$load$$

b$)$ Find the power factor at the $$source$$

c$)$ Find the complete phasor form of the line$-$to$-$line voltage V$\_$ab at the $$source$$