How would I calcluate a surface integral in dimensions greater than 3.(adsbygoogle = window.adsbygoogle || []).push({});

For example, from the definition of a surfrace integral over a vector field: http://en.wikipedia.org/wiki/Surface_integral#Surface_integrals_of_vector_fields

To compute the surface integral, I would first need a vector normal to the vector field. In R^3 this is just done by using the cross product. Is there a general way to find a normal vector when not in R^3, since the cross product is no longer valid?

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# Surface integrals in R^n, n>3

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