My book states the following:

A Boeing 737 aircraft maintains a constant airspeed of 500 miles per hour headed due south. The jet stream is 80 miles per hour in the northeasterly direction.

Express the velocity v of the 737 relative to the air.

Answer: The velocity of the 737 relative to the air is v = -500j

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I'm confused about this answer. If we want to calculated the speed of the plane relative to the air, wouldn't that mean relative to the wind traveling northeast at 80mph? In which case, we would have to figure out how fast the plane is going south with the wind traveling northeast (the wind would be hitting the plane at a 45 degree angle). We would also have to figure out how much the wind is slowing the plane down.

At least this is how I interpret "relative to the air" as. What am I missing? Could someone explain this relativity to me?