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I realise that this may seem like a really simple question but it's really driving me crazy. In my A-level maths we've just started looking at the cross product and I understand how to calculate it, it's application in calculating areas ect but I find myself not understanding what the product itself actually represents.

Could someone please help clarify this for me? I do not understand why the product represents a vector perpendicular to the vectors being crossed.

Thanks,

Oscar