A y-connected balanced three-phase sources is feeding a balanced three phase load. The voltage and current of the source coil are () = 340 sin(377 + 0.5236) () = 100 sin(377 + 0.87266) . Calculate the power factor at the source side, the three-phase real and reactive power delivered to the load, and the load impedance (if the load is connected in delta configuration).

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

one "light year" is the distance that light travels, through vacuum, in one julian year.   that's 365.25 days, of 24 hours each.