- #1
jink
- 7
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While using the ∇ operator, most of the times we can treat it as a vector. I came across a few formulae(basically product rules)..
where A and B are vectors
I wanted to know if there is any direct way of deriving it. By direct I mean assuming the basic vector identity
. Any other better way is also fine. I derived it by splitting each of the vectors A, B, and ∇(although this is not truly a vector) in their orthogonal components and then doing the appropriate cross products.
Code:
∇×([B]A[/B]×[B]B[/B])=([B]B[/B].∇)[B]A[/B]-([B]A[/B].∇)[B]B[/B]+[B]A[/B](∇.[B]B[/B])-[B]B[/B](∇.[B]A[/B])
I wanted to know if there is any direct way of deriving it. By direct I mean assuming the basic vector identity
Code:
[B]C[/B]×([B]B[/B]×[B]A[/B])=[B]B[/B]([B]C[/B].[B]A[/B])-[B]A[/B]([B]C[/B].[B]B[/B])