(d) Let y and be scalar fields. Prove that V (Vy x V) = 0. (e) R=xi + yj + zk and let r = Prove that V x (p(r)R) = 0 ||R||. Let y be a real-valued function of one variable.
(d) Let y and be scalar fields. Prove that V (Vy x V) = 0. (e) R=xi + yj + zk and let r = Prove that V x (p(r)R) = 0 ||R||. Let y be a real-valued function of one variable.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Do only part d ,e
Transcribed Image Text:Exercise 5. DIVERGENCE AND CURL
(a) Compute V · F and V x F and verify explicitly that V (V x F) = 0.
F = sinh(x)i + cosh(ryz)j – (x + y + z)k
(b) Compute Vy and verify explicitly that V x (Vy) = 0.
p(x, y, z) = x cos(x+ y+ z)
%3D
(c) Let y be a scalar field and F a vector field. Derive expressions for V (yF) and V x (YF) in terms of
operations applied to y and F.
(d) Let o and be scalar fields. Prove that
V. (Vy x V%) = 0.
%3D
(e) R=xi + yj + zk and let r =
Prove that V x (p(r)R) = 0
||R||. Let y be a real-valued function of one variable.
%3D
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