7) Consider a vector field F(x, y, z) = 3yi − xz j + yz².k. Let S be an equation of 2z = x²+y² located below z = 2, with downward orientation, then, i) show thatƑ · dr = −12 sin² 0-8 cos² 0. Then calculate fF.dr. (Ans: 207) с ii) show that curl.Fn =. 1 = z²x + x² + z +3. Then, evaluate ff curl.F-n ds. (Ans: 207)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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7) Consider a vector field F(x, y, z) = 3µi − xz_ j + yz²k. Let S be an equation of 2z = x² +y² located
below z = 2, with downward orientation, then,
i) show that_F · dr = −12 sin² 0 - 8 cos² . Then calculate fF.dr. (Ans: 207)
с
ii) show that curl.„F .n = z²x+x² +z+3. Then, evaluate ff curl.F -n ds. (Ans: 207)
S
Transcribed Image Text:7) Consider a vector field F(x, y, z) = 3µi − xz_ j + yz²k. Let S be an equation of 2z = x² +y² located below z = 2, with downward orientation, then, i) show that_F · dr = −12 sin² 0 - 8 cos² . Then calculate fF.dr. (Ans: 207) с ii) show that curl.„F .n = z²x+x² +z+3. Then, evaluate ff curl.F -n ds. (Ans: 207) S
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