   Chapter 16.1, Problem 2E

Chapter
Section
Textbook Problem

Sketch the vector field F by drawing a diagram like Figure 5 or Figure 9.2. F(x, y) = 1 2 x i + y j

To determine

To sketch: The vector field F for equation F(x,y)=12xi+yj .

Explanation

Given data:

F(x,y)=12xi+yj

Formula used:

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

Write the formula for length of the two dimensional vector.

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

Consider the given vector field.

F(x,y)=12xi+yj=12x,y

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

|F(x,y)|=(12x)2+(y)2=14x2+y2

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)|=14x2+y2 F(x,y)=〈12x,y〉 (0,0) 0 〈0,0〉 (1,0) 0.5 〈12,0〉 (−1,0) 0.5 〈−12,0〉 (2,0) 1 〈1,0〉 (−2,0) 1 〈−1,0〉 (0,1) 1 〈0,1〉 (0,−1) 1 〈0,−1〉 (1,1) 1

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