Let S be the portion of the plane 2x + 3y + z = 3 lying between the points (-1, 1, 2), (2, 1, -4), (2, 3, -10), and (-1, 3, -4). Find parameterizations for both the surface S and its boundary as. Be sure that their respective orientations are compatible with Stokes' theorem. from (-1, 1, 2) to (2, 1, -4) S,(t) tE [0, 1) from (2, 1, -4) to (2, 3, -10) S2(t) tE[1, 2) from (2, 3, -10) to (-1, 3, -4) S,(t) = tE [2, 3) from (-1, 3, -4) to (-1, 1, 2) s,(t) tE [3, 4) boundary Ф(и, v) uE [-1, 2], v E [1, 3] II
Let S be the portion of the plane 2x + 3y + z = 3 lying between the points (-1, 1, 2), (2, 1, -4), (2, 3, -10), and (-1, 3, -4). Find parameterizations for both the surface S and its boundary as. Be sure that their respective orientations are compatible with Stokes' theorem. from (-1, 1, 2) to (2, 1, -4) S,(t) tE [0, 1) from (2, 1, -4) to (2, 3, -10) S2(t) tE[1, 2) from (2, 3, -10) to (-1, 3, -4) S,(t) = tE [2, 3) from (-1, 3, -4) to (-1, 1, 2) s,(t) tE [3, 4) boundary Ф(и, v) uE [-1, 2], v E [1, 3] II
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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![Let S be the portion of the plane 2x + 3y + z = 3 lying between the points (-1, 1, 2), (2, 1, -4), (2, 3, -10), and
(-1, 3, -4). Find parameterizations for both the surface S and its boundary as. Be sure that their respective orientations
are compatible with Stokes' theorem.
from (-1, 1, 2) to (2, 1, -4)
S,(t)
tE [0, 1)
from (2, 1, -4) to (2, 3, -10)
S2(t)
tE[1, 2)
from (2, 3, -10) to (-1, 3, -4)
S,(t) =
tE [2, 3)
from (-1, 3, -4) to (-1, 1, 2)
s,(t)
tE [3, 4)
boundary
Ф(и, v)
uE [-1, 2], v E [1, 3]
II](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19331858-c67c-414f-8328-5459040eae8a%2Fa413ae69-09ce-47b1-97b5-b17d000cf75f%2Fza3q18a.png&w=3840&q=75)
Transcribed Image Text:Let S be the portion of the plane 2x + 3y + z = 3 lying between the points (-1, 1, 2), (2, 1, -4), (2, 3, -10), and
(-1, 3, -4). Find parameterizations for both the surface S and its boundary as. Be sure that their respective orientations
are compatible with Stokes' theorem.
from (-1, 1, 2) to (2, 1, -4)
S,(t)
tE [0, 1)
from (2, 1, -4) to (2, 3, -10)
S2(t)
tE[1, 2)
from (2, 3, -10) to (-1, 3, -4)
S,(t) =
tE [2, 3)
from (-1, 3, -4) to (-1, 1, 2)
s,(t)
tE [3, 4)
boundary
Ф(и, v)
uE [-1, 2], v E [1, 3]
II
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