Chapter 14: Q 2 (page 1153)

For any vector $F$ field in $R^{2}$ or $R^{3}$ ,
localid="1651016641773" $d i v (c u r l F) ==.$

Short Answer

Expert verified

The required answer is :-

For any vector field in $R^{2}$ or $R^{3}$

$d i v (c u r l F) = \nabla \cdot (\nabla \times F) = 0 .$

Step by step solution

Step 1. Given Information

We have given the following statement :-

$d i v (c u r l F) =______=______.$

Step 2. Complete the statement

We have to complete the given statement :-

$d i v (c u r l F) =______=______.$

$F = \{F_{1} (x, y, z), F_{2} (x, y, z)\} i n R^{2} o r F = \{F_{1} (x, y, z), F_{2} (x, y, z), F_{3} (x, y, z)\} i n R^{3}$

Here $F_{i}' s$ , $i = 1, 2, 3$ have continuous second order partial derivative.

We know that $c u r l F = \nabla \times F$ and $d i v F = \nabla \cdot F$

So that $d i v (c u r l F) = \nabla \cdot (\nabla \times F)$

We can easily get that :-

$\nabla \times F = 0 \Rightarrow \nabla \cdot (\nabla \times F) = 0$

So our final answer is :-

$d i v (c u r l F) = \nabla \cdot (\nabla \times F) = 0 .$

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For any vector $F$ field in $R^{2}$ or $R^{3}$ ,
localid="1651016641773" $d i v (c u r l F) ==.$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Complete the statement

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For any vector Ffield in R2 or R3, localid="1651016641773" divcurlF=______=______.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Complete the statement

One App. One Place for Learning.

Most popular questions from this chapter

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For any vector $F$ field in $R^{2}$ or $R^{3}$ ,
localid="1651016641773" $d i v (c u r l F) ==.$