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Give an example of a vector field F such that curl(F) = V x F is not perpendicular to F.

Give an example of a vector field F such that curl(F) = V x F is not perpendicular to F.

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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(a) Give an example of a vector field F such that curl(F) = V × F is not perpendicular to F. (b) Fix a real number 3 > 0. Compute the integral -22/2 cos(ßt) dt by considering the circulation of F(x, y) = e(v-a*)/2 (cos(xy), sin(xy)) around the bound- ary of the rectangle R = {(x, y)|-a <x < a,0 <yS B} and then taking the limit of the result as a → ∞. (You may freely use the famous fact that f e-t/2 dt = /2n.)
Transcribed Image Text:(a) Give an example of a vector field F such that curl(F) = V × F is not perpendicular to F. (b) Fix a real number 3 > 0. Compute the integral -22/2 cos(ßt) dt by considering the circulation of F(x, y) = e(v-a*)/2 (cos(xy), sin(xy)) around the bound- ary of the rectangle R = {(x, y)|-a <x < a,0 <yS B} and then taking the limit of the result as a → ∞. (You may freely use the famous fact that f e-t/2 dt = /2n.)
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