IGNOU PHE 4 2018 - Show that for two scalar fields f and g:∇ x ( f ∇g) +

Question

Show that for two scalar fields f and g:

∇ x ( f ∇g) + ∇ x (g ∇f ) = 0

25 Jan 2018

Answer :

Word Count : 342

The expression you provided involves the curl of a vector field. Let’s break it down and use the properties of vector calculus to understand it better. We are given the two scalar fields \( f \) and \( g \), and we need to show that: \[ \nabla \times (f \nabla g) + \nabla \times (g \nabla f) = 0 \] ### Step 1: Use the product rule for the curl of

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