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user41048 3 weeks ago

Is cross product of del ∇ x ∇ is zero in vectors?

I came across a vector term like

∇(∇ X F) = 0 

So I though to solve it like

M  = ∇.(∇ x F) 
   = F .( ∇ x ∇) - ∇.(∇ X F ) 
   = F .( ∇ x ∇) - M
2M = F .( ∇ x ∇) = 0 **(Here I suppose  ∇ x ∇ must be ZERO)** .

so

∇(∇ X F) =0 

Is this is true that ∇ x ∇ = 0 ?

Answers


Charles Bretana 3 weeks ago

From Wikipedia,

If two vectors have the same direction (or have the exact opposite direction from one another, i.e. are not linearly independent) or if either one has zero length, then their cross product is zero.

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