# About Nabla and index notation

## Homework Statement

Can I, for all purposes, say that Nabla, on index notation, is $$\partial_i e_i$$ and treat it like a vector when calculating curl, divergence or gradient?
For example, saying that $$\nabla \times \vec{V} = \partial_i \hat{e}_i \times V_j \hat{e}_j = \partial_i V_j (\hat{e}_i \times \hat{e}_j) = \partial_i V_j \epsilon_{ijk} \hat{e}_k$$
I have a feeling that is wrong, I've found all kinds of variations of this notation on the internet, almost no one seems to use the unit vectors, and that confuses me, being a total beginner on this kind of notation.

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## Answers and Replies

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