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What does a vector cross product mean in physical terms. Vector addition is quite easy to understand. I don't think the cross product is 'multiplication of vectors' as multiplication can be broken down into a series of additions at least for scalars.

Is the cross product simply a definition such that the product of 2 different components of a 2 vectors result in a multiplication of the magnitude in a direction perpendicular to the plane of the original vector components?

I don't really understand this in physical terms. All the books i have read have explained it in the above way.