Question

Q) a) Show that the vector field F = (12x^2y + 6z^2, 4x^3-20yz, 12xz-10y^2) is irrotational, that is ∇ x F = 0. (b) Find a potential function for F. (c) Evaluate the work integral ∫ F. dr, where C is a path running from the origin to the point (1,2,1).

Name: q a show that the vector field f 12x2y 6z2 4x3 20yz 12xz 10y2 is irrotational that is x f 0 b find a potential function for f c evaluate the work integral f dr where c is a path running from 49005
Uploaded: 2023-08-29T16:44:02-08:00
Duration: 7 min 18 s
Channel: Adi S
Description: q a show that the vector field f 12x2y 6z2 4x3 20yz 12xz 10y2 is irrotational that is x f 0 b find a potential function for f c evaluate the work integral f dr where c is a path running from 49005

          Q) a) Show that the vector field F = (12x^2y + 6z^2, 4x^3-20yz, 12xz-10y^2) is irrotational, that is ∇ x F = 0.
(b) Find a potential function for F.
(c) Evaluate the work integral ∫ F. dr, where C is a path running from the origin to the point (1,2,1).

Added by Jason W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/29/2023

Step 1

Step 1: To show that the vector field F is irrotational, we need to calculate the curl of F, denoted as ∇ x F. Show more…

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Q) a) Show that the vector field F = (12x^2y + 6z^2, 4x^3-20yz, 12xz-10y^2) is irrotational, that is ∇ x F = 0. (b) Find a potential function for F. (c) Evaluate the work integral ∫ F. dr, where C is a path running from the origin to the point (1,2,1).