You could exit the solar system in an orbit that goes through the perpendicular plane, which is not quite going straight North, just like no spacecraft goes straight outwards either, they just move in orbits within Earth’s orbital plane or close to that. This is because this way you take advantage of Earths orbital speed and you have the opportunity to slingshot with other planets as they are all in similar planes.
To move in the perpendicular plane it would mean you have to cancel Earths orbital speed itself so it’s wasteful, but maybe feasible. To go straight North or straight outwards means you have to fight gravity constantly so it’s extremely inneficient and not feasible at all.
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