So I've seen that the expansion for (∇×A)×A is (A⋅∇)A−1/2(∇(A⋅A)) . [Given that A is a vector]
Now I guess it's just really late in the night, but I can't make sense of the answer - if a vector dotted with itself is a scalar, it can't have a divergence. so what's the meaning of the second term in this expansion (specifically - ∇(A⋅A) )?
Here is an example of where one can find the identity. I must be missing something, but I don't know what it is!