Why do we define vector cross product stack exchange?
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linear algebra - Why does cross product give a vector which is ... That's because when you flip the plane the cross product is completely reversed, which means it's perpendicular to the plane. See what happens when you try to take (a×b)⋅a or (a×b)⋅b (you should get 0). If a vector is perpendicular to a basis of a plane, then it is perpendicular to that entire plane.
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