ector product of two vector fields: V × (F x G) = (V · G)F – (V · F)G + (G · V)F – (F · V)G %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Verify the following properties of the curl.
(i) Sum of two vector fields:
V × (F+ G) = V × F + V × G.
(ii) Product of a scalar field and a vector field:
V x (ƒF) = ƒV × F+ Vƒ × F.
(iii) Vector product of two vector fields:
V x (F x G) = (V · G)F – (V · F)G+ (G V)F – (F · V)G
%3D
Transcribed Image Text:2. Verify the following properties of the curl. (i) Sum of two vector fields: V × (F+ G) = V × F + V × G. (ii) Product of a scalar field and a vector field: V x (ƒF) = ƒV × F+ Vƒ × F. (iii) Vector product of two vector fields: V x (F x G) = (V · G)F – (V · F)G+ (G V)F – (F · V)G %3D
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