Concept explainers
Sketching a Vector Field In Exercises 1 and 2, find
To calculate:
Answer to Problem 1RE
Solution:
Explanation of Solution
Given:
Formula used:
Calculation:
Using (1), the magnitude of a vector function
The divergence of a vector field
We start by making a table showing the vector field at several points. The table shown is a small sample. The vector field lines at many other points should be calculated to get a representative vector field, which can be obtained by using a computer algebra system.
x |
-2 |
-1 |
0 |
0 |
1 |
2 |
y |
1 |
-1 |
-1 |
1 |
-1 |
-1 |
z |
1 |
1 |
1 |
1 |
1 |
1 |
Next, we draw line segments at the points to represent the vector field
The sketch of the representative vectors, is shown below
Interpretation: The vector field is irrotational in nature and has a positive divergence
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Chapter 15 Solutions
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