A force field F is given as F(x, y. z) = ay'i + bxyj + cz'k where a ,b and c are parameters satisfying abc <0 and 2a - b<0. A curve C is defined as the intersection of the plane z 2y-d and the cylinder x² + (y-1) = 4. where d is a non-zero parameter. Select appropriate values of the parameters a, b, c and d. a. Verify Stoke's theorem for the above-described scenario.
A force field F is given as F(x, y. z) = ay'i + bxyj + cz'k where a ,b and c are parameters satisfying abc <0 and 2a - b<0. A curve C is defined as the intersection of the plane z 2y-d and the cylinder x² + (y-1) = 4. where d is a non-zero parameter. Select appropriate values of the parameters a, b, c and d. a. Verify Stoke's theorem for the above-described scenario.
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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Transcribed Image Text:A force field F is given as F(x, y, z) = ay'i + bxyj + cz'k where a ,b
and e are parameters satisfying abc < 0 and 2a – b< 0. A curve C is defined
as the intersection of the plane z = 2y-d and the cylinder x² + (y- 1) =
4, where d is a non-zero parameter. Select appropriate values of the
parameters a, b, c and d.
%3D
a. Verify Stoke's theorem for the above-described scenario.
b. Choose TWO (2) points P and Q on the curve C and evaluate the work
done by the force field F along the segment PQ.
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