Let F be a smooth 2-dimensional vector field defined on an open set U in the plane containing a point P . Let r(t) be the field line of F that passes through P . Assume that: • F has constant magnitude 1 on a neighbourhood of P , • the field line r(t) has curvature a at P . How to find the curl of F at P with a complete proof?

Let F be a smooth 2-dimensional vector field defined on an open set U in the plane containing a point P . Let r(t) be the field line of F that passes through P . Assume that: • F has constant magnitude 1 on a neighbourhood of P , • the field line r(t) has curvature a at P . How to find the curl of F at P with a complete proof?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question

Let F be a smooth 2-dimensional vector field defined on an open set U in
the plane containing a point P . Let r(t) be the field line of F that passes through P .
Assume that:
• F has constant magnitude 1 on a neighbourhood of P ,
• the field line r(t) has curvature a at P .
How to find the curl of F at P with a complete proof?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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