Explanation Given: F = ∇ ( e − x 2 − y 2 − z 2 ) Formula: d i v ( F ) is given by: ∇ . F = 〈 ∂ ∂ x , ∂ ∂ y , ∂ ∂ z 〉 . 〈 P , Q , R 〉 = ∂ P ∂ x + ∂ Q ∂ y + ∂ R ∂ y = P x + Q y + R z c u r l ( F ) is given by ∇ . F = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z P Q R | = ( R y − Q z ) i − ( R x − P z ) j + ( Q x − P y ) k = 〈 ( R y − Q z ) i , − ( R x − P z ) , ( Q x − P y ) 〉 Let’s consider the given function F = ∇ ( e − x 2 − y 2 − z 2 ) Therefore d i v ( F ) is given by ∇ . F = 〈 ∂ ∂ x , ∂ ∂ y , ∂ ∂ z 〉 . 〈 e − x 2 − y 2 − z 2 〉 = ∂ e − x 2 − y 2 − z 2 ∂ x + ∂ e − x 2 − y 2 − z 2 ∂ y + ∂ e − x 2 − y 2 − z 2 ∂ z = e − x 2 − y 2 − z 2 ( − 2 x ) + e − x 2 − y 2 − z 2 ( − 2 y ) + e − x 2 − y 2 − z 2 ( − 2 z ) = − 2 e − x 2 − y 2 − z 2 ( x + y + z ) Therefore, ∇ ( ∇ . F ) is given by : ∇ ( ∇ . F ) = − 2 ( ∂ e − x 2 − y 2 − z 2 ( x + y + z ) ∂ x + ∂ e − x 2 − y 2 − z 2 ( x + y + z ) ∂ y + ∂ e − x 2 − y 2 − z 2 ( x + y + z ) ∂ z ) = − 2 ( − 2 x ( e − x 2 − y 2 − z 2 ) − 2 y ( e − x 2 − y 2 − z 2 ) − 2 z ( e − x 2 − y 2 − z 2 ) ) = 4 e − x 2 − y 2 − z 2 ( x + y + z ) c u r l ( F ) is given by ∇ ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17, Problem 13CRE

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Div (F) and curl (F) for $F = \nabla (e^{- x^{2} - y^{2} - z^{2}})$

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Chapter 17, Problem 12CRE

Chapter 17, Problem 14CRE

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Chapter 17 Solutions

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Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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Div (F) and curl (F) for F = ∇ ( e − x 2 − y 2 − z 2 )

Solution Summary: The author calculates div and curl for F =. The formula for d i v (F) is given by.

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To Calculate:

Div (F) and curl (F) for $F = \nabla (e^{- x^{2} - y^{2} - z^{2}})$

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Chapter 17 Solutions

Div (F) and curl (F) for F = ∇ ( e − x 2 − y 2 − z 2 )

Solution Summary: The author calculates div and curl for F =. The formula for d i v (F) is given by.

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To Calculate: Div (F) and curl (F) for F=∇(e−x2−y2−z2)

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Chapter 17 Solutions

To Calculate:

Div (F) and curl (F) for $F = \nabla (e^{- x^{2} - y^{2} - z^{2}})$