Explanation Given: Need to prove following condition curl ( f a ) = ∇ f × a where f is a differentiable function a is constant vector Formula used: 1) curl( F ) = ∇ × F 2) ∇ ( u F ) = ( ∇ u ) × F + u ( ∇ × F ) where u is a function and F is a vector. 3) For a constant vector a , ∇ × a = 0 . Calculation: Evaluating curl ( f a ) curl ( f a ) = ∇ × ( f a ) [using formula curl( F ) = ∇ × F ] =

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Chapter 18.2, Problem 31E

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Prove the given condition for a differentiable function and a constant vector.

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Chapter 18.2, Problem 30E

Chapter 18.2, Problem 32E

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Chapter 18 Solutions

CALCULUS (CLOTH)

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Chapter 18 Solutions