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(c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in part (a) and hence verify the identity in this case.

(c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in part (a) and hence verify the identity in this case.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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only solute question c ， please

(a) For all differentiable vector fields v(r) and w(r), use index notation to show that x W) + w X Χυ) ▼ (v.w) (v. V ) w w. ·V)v. υχ = (b) In the (x, y)-plane, sketch the vector fields v = (y, 2y, 0) and w= (x- -y, x+y, 0), clearly labelling which sketch is for which field. (c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in part (a) and hence verify the identity in this case.
Transcribed Image Text:(a) For all differentiable vector fields v(r) and w(r), use index notation to show that x W) + w X Χυ) ▼ (v.w) (v. V ) w w. ·V)v. υχ = (b) In the (x, y)-plane, sketch the vector fields v = (y, 2y, 0) and w= (x- -y, x+y, 0), clearly labelling which sketch is for which field. (c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in part (a) and hence verify the identity in this case.
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