F(x, y. =) = (y+: sin x, x+: cos y, cos x-sin y) and G(x, y, 2)={y-:sinx, x+zcos y, cos x+sin y} 1. Determine which vector field given above makes [(Páx+Qay +Rdz) independent of path. Then find potential function for that vector field.
F(x, y. =) = (y+: sin x, x+: cos y, cos x-sin y) and G(x, y, 2)={y-:sinx, x+zcos y, cos x+sin y} 1. Determine which vector field given above makes [(Páx+Qay +Rdz) independent of path. Then find potential function for that vector field.
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
Consider

Transcribed Image Text:F(x, y, =) = (y+: sin x, x+: cos y, cos x-sin y)
and G(x, y, 2)= {y-z sin x, x+z cos y, cosx+ sin y}
1. Determine which vector field given above makes [(Påx+Qciy + Rdz) independent of path.
Then find potential function for that vector field.
2. Find the work done by the vector field (force field) that is the answer for question 1. above
acting along the curve C from A to B. (Choose your own points A, B and curve C connecting these
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