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Engineering and Comp Sci Homework Help
How do I cross Del with (scalar*vector)?
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[QUOTE="Fido, post: 5559394, member: 602961"] [h2]Homework Statement [/h2] Show that for any scalar field α and vector field B: ∇ x (αB) = ∇α x B + α∇ x B[h2]Homework Equations[/h2] (∇ x B)[SUB]i[/SUB] = ε[SUB]ijk[/SUB] v[SUB]k,j[/SUB] (∇α)[SUB]i[/SUB] = α[SUB]i[/SUB] (u x v)[SUB]i[/SUB] = e[SUB]ijk[/SUB]u[SUB]j[/SUB]v[SUB]k[/SUB] [h2]The Attempt at a Solution[/h2] Since α is a scalar i wasn't quite sure how to cross it with ∇ So on the left side I have: ε[SUB]ijk[/SUB]B[SUB]k,j[/SUB] α[SUB]i[/SUB] 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: α[SUB]i[/SUB] x B + α∇ x B [/QUOTE]
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How do I cross Del with (scalar*vector)?
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