Q5. (a) Show that the curl of F is the vector field VxF=i-j-k
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Transcribed Image Text:Q5. (a) Show that the curl of F is the vector field
VxF=i-j-k
(b) Find a vector n (with positive z-component) normal to the surface o, in terms of
u, .
(c) Find the total flux of VXF across the surface o, via direct evaluation; i.e. calculate
the integral
(V x F). ds.
![Q6. (a) Show that the curve I(t) defined by the intersection between the surface o and the
cylinder x² + y² = 1, and parametrised by t € [0, 2π] can be written as
r(t) = (cost, sint, 1)
(b) Find the path integral of the vector field F along the path I'(t)
S
F.dr
(c) State the theorem that relates the answers to Q5 (c) and Q6(b), and explain how
this enables an interpretation of the curl of a vector field](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe781e991-850f-4092-9b36-3deffb65313c%2Fee0396d1-454d-4127-aa59-c73b8ba2a7e0%2Fjcw8r15_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q6. (a) Show that the curve I(t) defined by the intersection between the surface o and the
cylinder x² + y² = 1, and parametrised by t € [0, 2π] can be written as
r(t) = (cost, sint, 1)
(b) Find the path integral of the vector field F along the path I'(t)
S
F.dr
(c) State the theorem that relates the answers to Q5 (c) and Q6(b), and explain how
this enables an interpretation of the curl of a vector field
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