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Homework Statement
Show that for any scalar field α and vector field B:
∇ x (αB) = ∇α x B + α∇ x B
Homework Equations
(∇ x B)i = εijk vk,j
(∇α)i = αi
(u x v)i = eijkujvk
The Attempt at a Solution
Since α is a scalar i wasn't quite sure how to cross it with ∇
So on the left side I have:
εijkBk,j αi
I'm pretty sure I'm supposed to solve out the left side to get to the right because that what I did for the previous problem.
The right side all I could get it to simplify to was:
αi x B + α∇ x B