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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Sketch the vector field F by drawing a diagram like Figure 5 or Figure 9.

1. F(x, y) = 0.3 i − 0.4 j

To determine

To sketch: The vector field F for equation F(x,y)=0.3i0.4j .

Explanation

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)

Definition:

If two non zero vectors are scalar multiples of one another, then two non zero vectors are in parallel.

Write the expression for parallel vector of v .

v=nv (2)

Here,

n is any scalar multiple value.

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

|F(x,y)|=(0.3)2+(0.4)2=0.09+0.16=0.25=0.5

From definition, find the parallel vector for F(x,y)=0.3i0.4j .

Modify equation (2) as follows.

F(x,y)=nx,ny (3)

Consider the value of n=10

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Chapter 16 Solutions

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