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So,

[tex]\nabla X \vec{F}[/tex] is confusing me.

I understand that it can be used to tell whether a force is conservative in that, if the curl is 0 then the work done all all paths are the same... that's fine.

However,

I was looking at it, for example, in the context of the gravitational field. When drawing it out, one can see that the curl is indeed 0, and I've been told that it is proven by [tex]\nabla X \vec{F}[/tex], BUT from what I understand, and from what I've been told, the operator [tex] \nabla [/tex] has no direction, and thereby not a vector....

yet used in a vector product?

How can it even by setup in the first place if the operator isn't a vector?

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# Vector product - operator's a vector?

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