Determine whether the vector field F→(x,y,z)=zsin(8x)cos(5/y)i→+58zcos(8x)sin(5y)j→−18cos(8x)cos(5y)k→ is conservative and if it is find a potential function f(x,y)for the vector field. If the vector field is not conservative, enter NA. f(x,y,z)=

Determine whether the vector field F→(x,y,z)=zsin(8x)cos(5/y)i→+58zcos(8x)sin(5y)j→−18cos(8x)cos(5y)k→ is conservative and if it is find a potential function f(x,y)for the vector field. If the vector field is not conservative, enter NA. f(x,y,z)=

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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A: Solution :-

Question

Determine whether the vector field F→(x,y,z)=zsin(8x)cos(5/y)i→+58zcos(8x)sin(5y)j→−18cos(8x)cos(5y)k→ is conservative and if it is find a potential function f(x,y)for the vector field.

If the vector field is not conservative, enter NA.

f(x,y,z)=

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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