1. Let F = -yi + xj and let C be the unit circle oriented counterclockwise. (a) Show that F has constant magnitude on C. (b) Show that F is always tangent to the circle C. (c) Show that S¢F•dr = length of C.
1. Let F = -yi + xj and let C be the unit circle oriented counterclockwise. (a) Show that F has constant magnitude on C. (b) Show that F is always tangent to the circle C. (c) Show that S¢F•dr = length of C.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:1. Let F = -yi + xj and let C be the unit circle oriented counterclockwise.
(a) Show that F has constant magnitude on C.
(b) Show that F is always tangent to the circle C.
(c) Show that SoF·dr = length of C.
Expert Solution
Step 1
a.)
Let us parametrize C.
Since it's a circle of radius 1,
where
and so
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
