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 , z ) and is written as ∇ ⋅ F . Curl is the scalar product of the vector operator ∇ applied to the vector field F ( x , y , z ) and is written as ∇ × F . Given Info: F ( x , y , z ) = ( e y , s i n x , cos x ) 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 = ( e y , s i n x , cos x ) has components F 1 = e y , F 2 = s i n x , F 3 = cos x Divergence of the given vector F is, d i v ( F ) = ∇ ⋅ F ( x , y , z ) = ∂ F 1 ∂ x + ∂ F 2 ∂ y + ∂ F 3

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 17.1, Problem 29E

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Divergence and curl of the vector $F = (e^{y}, s i n x, \cos x)$

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Chapter 17.1, Problem 28E

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Divergence and curl of the vector F = ( e y , s i n x , cos x )

Solution Summary: The author explains that the vector differential operator, called "del", is defined as d i v = 0 and c u r l = ( sin x) j + ( co

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Divergence and curl of the vector $F = (e^{y}, s i n x, \cos x)$

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Chapter 17 Solutions

Divergence and curl of the vector F = ( e y , s i n x , cos x )

Solution Summary: The author explains that the vector differential operator, called "del", is defined as d i v = 0 and c u r l = ( sin x) j + ( co

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Divergence and curl of the vector F=(ey,sinx,cosx)

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Chapter 17 Solutions

Divergence and curl of the vector $F = (e^{y}, s i n x, \cos x)$