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Express the field D = (x² + y²)−¹(xax + yay) in cylindrical components and cylindrical variables.

Express the field D = (x² + y²)−¹(xax + yay) in cylindrical components and cylindrical variables.

Advanced Engineering Mathematics
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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1. Express the field D = (x² + y²)−¹(xax + yay) in cylindrical components and cylindrical variables. 2. a. Give the cartesian coordinates that extends from P(4,10°, 1) to Q(7,75°, 4) b. Give the vector in cylindrical coordinates at M (5,1,2) that extends N(2,4,6) c. How far is it from A(11,60°, -20) and B(30,125°, 10) 3. Transform each of the following vectors to cylindrical coordinates at the point specified: a. 5ax at P(4, 120°, 2) b. 5a, at Q(3,4,-1) C. 4ax 2ay - 4a₂ at A(2,3,5) - 4. Express the unit vector ax in spherical components at the point: a. P(2,1 rad, 0.8 rad.) b. P(3,2,-1) c. P(2.5,2π/9, 1.5)
Transcribed Image Text:1. Express the field D = (x² + y²)−¹(xax + yay) in cylindrical components and cylindrical variables. 2. a. Give the cartesian coordinates that extends from P(4,10°, 1) to Q(7,75°, 4) b. Give the vector in cylindrical coordinates at M (5,1,2) that extends N(2,4,6) c. How far is it from A(11,60°, -20) and B(30,125°, 10) 3. Transform each of the following vectors to cylindrical coordinates at the point specified: a. 5ax at P(4, 120°, 2) b. 5a, at Q(3,4,-1) C. 4ax 2ay - 4a₂ at A(2,3,5) - 4. Express the unit vector ax in spherical components at the point: a. P(2,1 rad, 0.8 rad.) b. P(3,2,-1) c. P(2.5,2π/9, 1.5)
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