Explanation The vector differential operator ∇, called "del" is defined as ∇= ∂ ∂ x i + ∂ ∂ y j + ∂ ∂ z k Divergence of vector field is the scalar product of the vector operator ∇ applied to the vector field F(x, y) and is written as ∇.F Curl is the scalar product of the vector operator ∇ applied to the vector field F(x, y) and is written as ∇× F. Given Info: F = sin ( x + z ) i − y e x z k Formula Used: d i v ( F ) = ∇. F ( x , y , z ) = ∂ F 1 ∂ x + ∂ F 2 ∂ y + ∂ F 3 ∂ z c u r l ( F ) = ∇× F = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z F 1 F 2 F 3 | = ( ∂ F 3 ∂ y − ∂ F 2 ∂ z ) i − ( ∂ F 3 ∂ x − ∂ F 1 ∂ z ) j + ( ∂ F 2 ∂ x − ∂ F 1 ∂ y ) k Calculation: The vector field F = sin ( x + z ) i − y e x z k has components F 1 = sin ( x + z ) , F 2 = 0 , F 3 = − y e x z Divergence of the given vector F is, ∇. F ( x , y , z ) = ∂ F 1 ∂ x + ∂ F 2 ∂ y + ∂ F 3 ∂ z = ∂ ∂ x ( sin ( x + z ) ) + ∂ ∂ y ( 0 ) + ∂ ∂ z ( − y e x z )

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.1, Problem 26E

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Divergence and curl of the vector $F = \sin (x + z) i - y e^{x z} k$

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Chapter 17.1, Problem 25E

Chapter 17.1, Problem 27E

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Chapter 17 Solutions

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Divergence and curl of the vector F = sin ( x + z ) i − y e x z k

Solution Summary: The author explains the scalar product of the vector differential operator, called "del".

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Divergence and curl of the vector $F = \sin (x + z) i - y e^{x z} k$

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Chapter 17 Solutions

Divergence and curl of the vector F = sin ( x + z ) i − y e x z k

Solution Summary: The author explains the scalar product of the vector differential operator, called "del".

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Divergence and curl of the vector F=sin(x+z)i−yexzk

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Chapter 17 Solutions

Divergence and curl of the vector $F = \sin (x + z) i - y e^{x z} k$