Explanation Calculation: The given curve C = { ( x , y ) : x 2 + y 2 = 1 } is a circle with radius 1. Let vectors that are tangential to C = { ( x , y ) : x 2 + y 2 = 1 } are 〈 − y , x 〉 , Then, 〈 y , x 〉 is a scalar multiple of the tangent vectors at y = 0 or at x = 0 and F = 〈 y , x 〉 is tangent to C = { ( x , y ) : x 2 + y 2 = 1 } at ( ± 1 , 0 ) and ( 0 , ± 1 ) . Thus, F ⋅ 〈 − y , x 〉 = 〈 y , x 〉 ⋅ 〈 − y , x 〉 = x 2 − y 2

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 14.1, Problem 20E

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Whether the points on the curve at which the vector field F=〈y,x〉 is tangent to C and normal to C or not.

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Chapter 14.1, Problem 19E

Chapter 14.1, Problem 21E

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Chapter 14 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 14.1 - How is a vector field F = f, g, h used to describe...Ch. 14.1 - Sketch the vector field F = x, y.Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Interpret the gradient field of the temperature...Ch. 14.1 - Two-dimensional vector fields Sketch the following...Ch. 14.1 - Two-dimensional vector fields Sketch the following...Ch. 14.1 - Two-dimensional vector fields Sketch the following...Ch. 14.1 - Two-dimensional vector fields Sketch the following...Ch. 14.1 - Two-dimensional vector fields Sketch the following...

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Whether the points on the curve at which the vector field F = 〈 y , x 〉 is tangent to C and normal to C or not.

Solution Summary: The author explains that the vector field F=langle x,yrangle is tangential to the curve C and normal to C.

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Whether the points on the curve at which the vector field F=〈y,x〉 is tangent to C and normal to C or not.

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Chapter 14 Solutions