T0.Tind the nux of the vector field k- across the sphere of radius R centered at origin, where F=(x,y,z) is the position vector ( Ans: 47TR*k) 17. Verify the Gauss Divergence theorem for the vector field F = k-, over the surface of the sphere x +y² +z² = R² where F = (x, y, z) is the position vector. (Ans: 4tR*k) %3D 18. Find the flux of the water through the parabolic cylinder y =x, between the planes x=0,z=D0,x%=3,z=2, if the velocity vector is F = yî+2j+ xzk m/ sec. (Ans: 69 m / sec %3D ) 19. If F =(2x-y+2z)î+(x+y-z)ĵ+(3x-2y-5z)k , calculate the circulation of F along the circle in the xy-plane of radius 2 and centre at origin. ( Ans: 87) 20. Using Green's theorem find the area of the region bounded by y=x and y =x+2.( Ans: 9/2) Scanned by CamScanner
T0.Tind the nux of the vector field k- across the sphere of radius R centered at origin, where F=(x,y,z) is the position vector ( Ans: 47TR*k) 17. Verify the Gauss Divergence theorem for the vector field F = k-, over the surface of the sphere x +y² +z² = R² where F = (x, y, z) is the position vector. (Ans: 4tR*k) %3D 18. Find the flux of the water through the parabolic cylinder y =x, between the planes x=0,z=D0,x%=3,z=2, if the velocity vector is F = yî+2j+ xzk m/ sec. (Ans: 69 m / sec %3D ) 19. If F =(2x-y+2z)î+(x+y-z)ĵ+(3x-2y-5z)k , calculate the circulation of F along the circle in the xy-plane of radius 2 and centre at origin. ( Ans: 87) 20. Using Green's theorem find the area of the region bounded by y=x and y =x+2.( Ans: 9/2) Scanned by CamScanner
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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Plz send answer for 18th and 19th
Transcribed Image Text:T0.Tind the nux of the vector field k- across the sphere of radius R centered at origin, where
F=(x,y,z) is the position vector ( Ans: 47TR*k)
17. Verify the Gauss Divergence theorem for the vector field F = k-, over the surface of the
sphere x +y² +z² = R² where F = (x, y, z) is the position vector. (Ans: 4tR*k)
%3D
18. Find the flux of the water through the parabolic cylinder y =x, between the planes
x=0,z=D0,x%=3,z=2, if the velocity vector is F = yî+2j+ xzk m/ sec. (Ans: 69 m / sec
%3D
)
19. If F =(2x-y+2z)î+(x+y-z)ĵ+(3x-2y-5z)k , calculate the circulation of F along
the circle in the xy-plane of radius 2 and centre at origin. ( Ans: 87)
20. Using Green's theorem find the area of the region bounded by y=x and y =x+2.( Ans:
9/2)
Scanned by CamScanner
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