a) Find the values of a,b,c which makef(x,y,z) = sin (xay°z©) a potential function for the vector fieldF(x.y,z)= 4 x³y'z? cos (x*y z7) i+ 7x*y®z7 cos (x*y'z?) j + 7x*y?z® cos (x*y'z7) ka=b=c=b) Find the work of F along the curve r(t)=(2t, e t(t – 1), e tt – 1)) for 0sts1.Do not approximate your answer. For example, leave sin (e ) as that, not 0.41.Work =F•dr =

Answered: Image /qna-images/answer/f6b64e3b-42c3-40ad-9620-7171ecc7dc49.jpg

a) Find the values of a,b,c which make f(x,y,z) = sin (xªy®z©) a potential function for the vector field F(x,y.z)= 4 x°y?z? cos (x*y"z7) i+ 7x*y®z7 cos (x*y'z?) j + 7 x*y?z® cos (x*y?z?) k a= b= c= b) Find the work of F along the curve r(t)= (2t, e t(t - 1), e t(t – 1)) for 0sts1. Do not approximate your answer. For example, leave sin (e) as that, not 0.41. Work = F• dr

a) Find the values of a,b,c which make f(x,y,z) = sin (xªy®z©) a potential function for the vector field F(x,y.z)= 4 x°y?z? cos (xy"z7) i+ 7xy®z7 cos (xy'z?) j + 7 xy?z® cos (x*y?z?) k a= b= c= b) Find the work of F along the curve r(t)= (2t, e t(t - 1), e t(t – 1)) for 0sts1. Do not approximate your answer. For example, leave sin (e) as that, not 0.41. Work = F• dr

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

a) Find the values of a,b,c which make
f(x,y,z) = sin (xay°z©) a potential function for the vector field
F(x.y,z)= 4 x³y'z? cos (x*y z7) i+ 7x*y®z7 cos (x*y'z?) j + 7x*y?z® cos (x*y'z7) k
a=
b=
c=
b) Find the work of F along the curve r(t)=(2t, e t(t – 1), e tt – 1)) for 0sts1.
Do not approximate your answer. For example, leave sin (e ) as that, not 0.41.
Work =
F•dr =

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