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(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 parametrie representation 1 = at, y= bt, z = et (0

(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 parametrie representation 1 = at, y= bt, z = et (0

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 13CR
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Question
Q5 vector field, In Cartesian coordinates, a vector fiekd takes the form F = 2rz1+ 2y=J+ (r² + y³) k This question concerns the vector fickd 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 parametrie 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 funetion U(1,y, 2) corresponding to F, such that F = -VU. (d) Hence, or otherwise, caleulate the value of the line integral of F along a path defined by the parametric equations 2 I= cos t, y = sin t, z=t (0<t< x). (Hint: You can use the potential function U caleulated in part (c) to evaluate this line integral.)
Transcribed Image Text:Q5 vector field, In Cartesian coordinates, a vector fiekd takes the form F = 2rz1+ 2y=J+ (r² + y³) k This question concerns the vector fickd 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 parametrie 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 funetion U(1,y, 2) corresponding to F, such that F = -VU. (d) Hence, or otherwise, caleulate the value of the line integral of F along a path defined by the parametric equations 2 I= cos t, y = sin t, z=t (0<t< x). (Hint: You can use the potential function U caleulated in part (c) to evaluate this line integral.)
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