Explanation Given: The given vector field equation is F ( x , y ) = y i + ( x + y ) j . Formula used: Consider a two-dimensional vector F = 〈 x , y 〉 . The expression for length of the two dimensional vector is | F ( x , y ) | = x 2 + y 2 ⋯ ( 1 ) . Calculation: Consider the given vector field. F ( x , y ) = y i + ( x + y ) j = 〈 y , ( x + y ) 〉 Find the length of F ( x , y ) using equation (1). | F ( x , y ) | = ( y ) 2 + ( x + y ) 2 ⋯ ( 2 ) Consider the line with y = − x . Rewrite the above equation as x = − y . Substitute − y for x in equation (2) as shown below. | F ( x , y ) | = y 2 + ( − y + y ) 2 = y 2 + 0 = y 2 = | y | Consider a certain interval of x as ( − 2 , 2 ) and y as ( − 2 , 2 ) to plot F ( x , y ) . The estimated values of | F ( x , y ) | and F ( x , y ) for different values of x and y are shown in Table 1. Table 1 ( x , y ) | F ( x , y ) | = | y | F ( x , y ) = 〈 y , ( x + y ) 〉 ( 0 , 0 ) 0 〈 0 , 0 〉 ( 1 , 0 ) 0 〈 0 , 1

Single Variable Essential Calculus: Early Transcendentals

2nd Edition

ISBN: 9781133112785

Author: James Stewart

Publisher: Cengage Learning

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Chapter 13.1, Problem 4E

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To sketch: The vector field F for equation F(x,y)=y i+(x+y) j.

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Chapter 13.1, Problem 3E

Chapter 13.1, Problem 5E

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Chapter 13 Solutions

Single Variable Essential Calculus: Early Transcendentals

Ch. 13.1 - Sketch the vector field F by drawing a diagram...Ch. 13.1 - Sketch the vector field F by drawing a diagram...Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Sketch the vector field F by drawing a diagram...Ch. 13.1 - Prob. 9E Ch. 13.1 - Sketch the vector field F by drawing a diagram...

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The vector field F for equation F ( x , y ) = y i + ( x + y ) j .

Solution Summary: The author sketched the vector field F for equation F(x,y) = y+y-rangle . The expression for length of the two-dimensional vector is langle

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To sketch: The vector field F for equation F(x,y)=y i+(x+y) j.

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Chapter 13 Solutions