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EXAMPLE 2 Normal and tangent vectors Let C be the circle x? + y? = a², where a > 0. (х, у) is a. Show that at each point of C, the radial vector field F (x, y) orthogonal to the line tangent to C'at that point. %3D |r| V? + y² (-у,х) V + y? b. Show that at each point of C, the rotation vector field G(x, y) is paralel to the line tangent to C at that point.

EXAMPLE 2 Normal and tangent vectors Let C be the circle x? + y? = a², where a > 0. (х, у) is a. Show that at each point of C, the radial vector field F (x, y) orthogonal to the line tangent to C'at that point. %3D |r| V? + y² (-у,х) V + y? b. Show that at each point of C, the rotation vector field G(x, y) is paralel to the line tangent to C at that point.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In the problem given, verify that ∇g(x, y) ⋅ G(x, y) = 0. In parts (a) and (b) of the problem, verify that | F| = 1 and |G| = 1 at all points excluding the origin.

EXAMPLE 2 Normal and tangent vectors Let C be the circle x? + y? = a², where a > 0. (х, у) is a. Show that at each point of C, the radial vector field F (x, y) orthogonal to the line tangent to C'at that point. %3D |r| V? + y² (-у,х) V + y? b. Show that at each point of C, the rotation vector field G(x, y) is paralel to the line tangent to C at that point.
Transcribed Image Text:EXAMPLE 2 Normal and tangent vectors Let C be the circle x? + y? = a², where a > 0. (х, у) is a. Show that at each point of C, the radial vector field F (x, y) orthogonal to the line tangent to C'at that point. %3D |r| V? + y² (-у,х) V + y? b. Show that at each point of C, the rotation vector field G(x, y) is paralel to the line tangent to C at that point.
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