c) The surface S is the portion of the plane x+y+z=1 in the first quadrant of the Oxyz Cartesian coordinate space. The directed straight lines from (1,0,0) to (0,0,1), (0,0,1) to (0,1,0) and (0,1,0) back to (1,0,0) are denoted by C, C, and C, respectively. The union of C, C, and C, form a closed path C with a particular direction. Use Stokes' theorem to evaluate the line integral (xy dx+z dy+ zydz). (Hint. The relation . F•dr = [[.V× F)•n do is given in Stokes' theorem.) %3D
c) The surface S is the portion of the plane x+y+z=1 in the first quadrant of the Oxyz Cartesian coordinate space. The directed straight lines from (1,0,0) to (0,0,1), (0,0,1) to (0,1,0) and (0,1,0) back to (1,0,0) are denoted by C, C, and C, respectively. The union of C, C, and C, form a closed path C with a particular direction. Use Stokes' theorem to evaluate the line integral (xy dx+z dy+ zydz). (Hint. The relation . F•dr = [[.V× F)•n do is given in Stokes' theorem.) %3D
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:(c) The surface S is the portion of the plane x+ y+z=1 in the first quadrant of the Oxyz
Cartesian coordinate space. The directed straight lines from (1,0,0) to (0,0,1), (0,0,1) to
(0,1,0) and (0,1,0) back to (1,0,0) are denoted by C, C, and C, respectively. The
union of C,, C, and C, form a closed path C with a particular direction. Use Stokes'
theorem to evaluate the line integral (xy dx+z dy+zydz).
(Hint. The relation F•dr= ||.(Vx F)•n do is given in Stokes' theorem.)
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