3. Solve the following showing full and complete procedure a) A particle moves along the triangle with vertices (1,0,0), (0,1,0) and (0,0,1) under the influence of the force field: counterclockwise F(x,y,z)= (x+y²)į + (y+z²)j + (z+ x²)k. Find the work done b) Use the divergence (Gauss') theorem to calculate the flux of F across S where F(x,y,z) = x² siny į + xcosy j - xz siny k and S is the "fat sphere” x³ + y² + z³ = 8 (a dice) c) Calculate the flux of the vector field: F(x,y,z) = 4xz i + xyz j + 3z k across the outer side of the surface S, z² = x² + y², 0≤z≤4
3. Solve the following showing full and complete procedure a) A particle moves along the triangle with vertices (1,0,0), (0,1,0) and (0,0,1) under the influence of the force field: counterclockwise F(x,y,z)= (x+y²)į + (y+z²)j + (z+ x²)k. Find the work done b) Use the divergence (Gauss') theorem to calculate the flux of F across S where F(x,y,z) = x² siny į + xcosy j - xz siny k and S is the "fat sphere” x³ + y² + z³ = 8 (a dice) c) Calculate the flux of the vector field: F(x,y,z) = 4xz i + xyz j + 3z k across the outer side of the surface S, z² = x² + y², 0≤z≤4
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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show full and complete procedure HANDWRITTEN only. Please answer parts a), b) and c) as they are subparts of the same question
Transcribed Image Text:3. Solve the following showing full and complete procedure
a) A particle moves along the triangle with vertices (1,0,0), (0,1,0) and (0,0,1)
counterclockwise under the influence of the force field:
F(x,y,z)= (x+y²)į + (y+z²)j + (z+ x²)k. Find the work done
b) Use the divergence (Gauss') theorem to calculate the flux of F across S where
F(x,y,z) = x² siny į + xcosy j - xz siny k and S is the "fat sphere” x³ + y² + z³ = 8 (a
dice)
c) Calculate the flux of the vector field: F(x,y,z) = 4xz i + xyz j + 3z k across the outer side
of the surface S, z² = x² + y²,0 ≤z≤4
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