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Q5 vector field, In Cartesian coordinates, a vector field takes the form F = 2rzi+ 2yzj+ (r² +y*)k This question concerns the vector field F defined in Question 5. (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation I = at, y= bt, z= et (0

Q5 vector field, In Cartesian coordinates, a vector field takes the form F = 2rzi+ 2yzj+ (r² +y*)k This question concerns the vector field F defined in Question 5. (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation I = at, y= bt, z= et (0

Advanced Engineering Mathematics
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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Q5 vector field, In Cartesian coordinates, a vector field takes the form F = 2rzi+ 2yzj+ (r² +y*) k This question concerns the vector field F defined in Question 5. (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation I = at, y = bt, z= et (0 <t < 1). (c) Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(1,y, 2) corresponding to F, such that F = -VU. (d) Hence, or otherwise, calculate the value of the line integral of F along a path defined by the parametric equations I= Cos t, y = sin t, z 2 z=t (0 <t<n). (Hint: You can use the potential function U calculated in part (c) to evaluate this line integral.)
Transcribed Image Text:Q5 vector field, In Cartesian coordinates, a vector field takes the form F = 2rzi+ 2yzj+ (r² +y*) k This question concerns the vector field F defined in Question 5. (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation I = at, y = bt, z= et (0 <t < 1). (c) Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(1,y, 2) corresponding to F, such that F = -VU. (d) Hence, or otherwise, calculate the value of the line integral of F along a path defined by the parametric equations I= Cos t, y = sin t, z 2 z=t (0 <t<n). (Hint: You can use the potential function U calculated in part (c) to evaluate this line integral.)
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