12. (a) Consider again the vector field in Exercise 8 and its curl. Sketch the vector field and use your pic- ture to explain geometrically why the curl is as you calculated. (b) Use geometry to determine V × F, where F = (xi + yj + zk) /x² + y² + z² (c) For F as in part (b), verify your intuition by explic- itly computing V × F.
12. (a) Consider again the vector field in Exercise 8 and its curl. Sketch the vector field and use your pic- ture to explain geometrically why the curl is as you calculated. (b) Use geometry to determine V × F, where F = (xi + yj + zk) /x² + y² + z² (c) For F as in part (b), verify your intuition by explic- itly computing V × F.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:12. (a) Consider again the vector field in Exercise 8 and
its curl. Sketch the vector field and use your pic-
ture to explain geometrically why the curl is as you
calculated.
(b) Use geometry to determine ▼ × F, where F =
(xi+ yj + zk)
Vx² + y² + z²
(c) For Fas in part (b), verify your intuition by explic-
itly computing V × F.
8. F = xi+ yj + zk
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