Cross Product and Triple Scalar Product

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This isn't homework, but I worked this out to become more fluent with expressing these operations using sums, indices, etc. This is from my Vector Analysis course, and the professor said understanding this would make the rest of the course smooth sailing if I get all these concepts down.

I'm fairly confident on A X B since I checked it with my notes from class.

However, for the triple scalar product, in our notes we started with b-sub j and c-sub k. I started with b-sub i and c-sub j, so the order of my indices were different. I also worked out the operations separately then combined them at the end. In class, we wrote everything out all at once. I get the feeling that's the better way to do it. Thanks for any help.

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