Chapter 14: Q. 13 (page 1095)

Consider the vector field $F (x, y, z) = (y z, x z, x y)$ . Find a vector field $G (x, y, z)$ with the property that, for all points in role="math" localid="1650383268941" $ℝ^{3}, G (x, y, z) = 2 F (x, y, z)$ .

Short Answer

Expert verified

A vector field $G (x, y, z) = 2 y z, 2 x z, 2 x y$

Step by step solution

Step 1.Given Information

Consider the vector field $F (x, y, z) = (y z, x z, x y)$ . Find a vector field $G (x, y, z)$ with the property that, for all points in $ℝ^{3}, G (x, y, z) = 2 F (x, y, z)$ .

Step 2. The value of F(x,y,z)=(yz,xz,xy)

Now finding a vector field $G (x, y, z)$

As we know that

$G (x, y, z) = 2 F (x, y, z) G (x, y, z) = 2 (y z, x z, x y) G (x, y, z) = 2 y z, 2 x z, 2 x y$

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Consider the vector field $F (x, y, z) = (y z, x z, x y)$ . Find a vector field $G (x, y, z)$ with the property that, for all points in role="math" localid="1650383268941" $ℝ^{3}, G (x, y, z) = 2 F (x, y, z)$ .

Short Answer

Step by step solution

Step 1.Given Information

Step 2. The value of F(x,y,z)=(yz,xz,xy)

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Consider the vector field F(x,y,z)=(yz,xz,xy). Find a vector field G(x,y,z) with the property that, for all points in role="math" localid="1650383268941" ℝ3,G(x,y,z)=2F(x,y,z).

Short Answer

Step by step solution

Step 1.Given Information

Step 2. The value of F(x,y,z)=(yz,xz,xy)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Probability and Statistics

Geometry

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Consider the vector field $F (x, y, z) = (y z, x z, x y)$ . Find a vector field $G (x, y, z)$ with the property that, for all points in role="math" localid="1650383268941" $ℝ^{3}, G (x, y, z) = 2 F (x, y, z)$ .