   Chapter 16.1, Problem 4E

Chapter
Section
Textbook Problem

Sketch the vector field F by drawing a diagram like Figure 5 or Figure 9.4. F(x, y) = y i + (x + y) j

To determine

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

Explanation

Given data:

F(x,y)=yi+(x+y)j

Formula used:

Consider a two-dimensional vector F=x,y .

Write the expression for length of the two dimensional vector.

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

Consider the given vector field.

F(x,y)=yi+(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 .

x=y

Substitute y for x in equation (2),

|F(x,y)|=y2+(y+y)2=y2+0=y2=|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〉 (−1,0) 0 〈0,−1〉

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