Explanation Given: F → = 〈 2 x y z , x 2 z , x 2 y z 〉 is a vector field. Formula used: If f is a potential function for the vector field F → then F → = ∇ → f Where, ∇ → = 〈 ∂ ∂ x , ∂ ∂ y 〉 Curl of a vector is given by ∇ → × F → If Curl F → = 0 F → is conservative then potential function exists. If Curl F → ≠ 0 mean F → is not conservative then potential function does not exist. Calculation: Checking for existence of the potential function by taking Curl of the given potential function, F → = 〈 2 x y z , x 2 z , x 2 y z 〉 we get- = ∇ → × F → = | i ^

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.1, Problem 44E

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Potential function for the vector field $\vec{F} = 〈 2 x y z, x^{2} z, x^{2} y z 〉$ by inspection or show that one does not exist.

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Chapter 17.1, Problem 43E

Chapter 17.1, Problem 45E

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Potential function for the vector field F → = 〈 2 x y z , x 2 z , x 2 y z 〉 by inspection or show that one does not exist.

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Potential function for the vector field $\vec{F} = 〈 2 x y z, x^{2} z, x^{2} y z 〉$ by inspection or show that one does not exist.

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