Write True if the statement is always true. Otherwise, write False. (a) Any sphere with radius 2 has equation p= 2 in spherical coordinates. (b) There is a function o such that Vo (ry.r2+ :.y). %3D (c) If-C denotes the curve C traced in the opposite direction, then: L(a.u) ds = (r, y) ds. (d) If there is one closed path C such that F dR = 0, then F is a conservative vector field. (c) Stokes' Theorem relates the flux of a vector field F across a surface S with the line integral of Fon the boundary curve of S.
Write True if the statement is always true. Otherwise, write False. (a) Any sphere with radius 2 has equation p= 2 in spherical coordinates. (b) There is a function o such that Vo (ry.r2+ :.y). %3D (c) If-C denotes the curve C traced in the opposite direction, then: L(a.u) ds = (r, y) ds. (d) If there is one closed path C such that F dR = 0, then F is a conservative vector field. (c) Stokes' Theorem relates the flux of a vector field F across a surface S with the line integral of Fon the boundary curve of S.
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:vectors.
Write True if the statement is always true. Otherwise, write False.
(a) Any sphere with radius 2 has equation p= 2 in spherical coordinates.
(b) There is a function o such that Vo = (ry, r + . y).
(c) If -C denotes the curve C traced in the opposite direction, then:
| (r.y) ds =
S(r. y) ds.
(d) If there is one closed path C such that
F.AR = 0, then F is a
conservative vector field.
(e) Stokes Theorem relates the flux of a vector field F across a surface S
with the line integral of F on the boundary curve of S.
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