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Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

||Vel_jet_r|| =  465.993 mph

Step-by-step explanation:

We need to decompose the velocity of the wind into a component that can be added  (or subtracted from the velocity of the jet)

The velocity of the jet

500 mph North

Velocity of the wind

50 mph SouthEast = 50 cos(45) East + 50 sin (45) South

South = - North

Vel_ wind = 50 cos(45) mph  East  -  50 sin (45) mph North

Vel _wind =  35.35 mph  East  -  35.35 mph North

This means that the resulting  velocity of the jet is equal to

Vel_jet_r =  (500 mph - 35.35 mph) North + 35.35 mph East

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

An the jet has a magnitude velocity of

||Vel_jet_r|| =  sqrt ((464.645 mph)^2 + (35.35 mph)^2)

||Vel_jet_r|| =  465.993 mph

w'x is 0.

hope it