   Chapter 16.1, Problem 12E

Chapter
Section
Textbook Problem

Match the vector fields F with the plots labeled I-IV. Give reasons for your choices.12. F(x, y) = ⟨y, x − y⟩ To determine

To match: The vector field F(x,y)=y,xy with the plots labeled as I-IV.

Explanation

Given data:

The vector field F(x,y)=y,xy.

Formula used:

The expression for the length of the two-dimensional vector F=x,y,

|F(x,y)|=x2+y2 (1)

Find the length of F(x,y) using equation (1).

|F(x,y)|=(y)2+(xy)2

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

 Quadrant (x,y) |F(x,y)|=(y)2+(x−y)2 F(x,y)=〈y,x−y〉 I (0,0) 0 〈0,0〉 (1,0) 1 〈0,1〉 (2,0) 2 〈0,2〉 (0,1) 2 〈1,−1〉 (1,1) 1 〈1,0〉 (0,2) 22 <

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