Match each of the following planar vector fields with the corresponding plot. Note that the vectors are scaled to avoid overlap. 3 2 1 of -2 Incorrect 4 3 2 1 0 -1 -2 -3 3 N F(x, y) = 5yj 0 1 F(x, y) = -5yj 0 Answer Bank 2 2 3 3 2 1 0 -1 2 0 -2 T A L 3 1 -2 1 1 V F(x, y) = 5yi -1 1 1 A ↓ F(x, y) = -5 yi 1 0 1 1 A 1 2 3 4
Match each of the following planar vector fields with the corresponding plot. Note that the vectors are scaled to avoid overlap. 3 2 1 of -2 Incorrect 4 3 2 1 0 -1 -2 -3 3 N F(x, y) = 5yj 0 1 F(x, y) = -5yj 0 Answer Bank 2 2 3 3 2 1 0 -1 2 0 -2 T A L 3 1 -2 1 1 V F(x, y) = 5yi -1 1 1 A ↓ F(x, y) = -5 yi 1 0 1 1 A 1 2 3 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The image contains a task to match planar vector fields with their corresponding plots. There are four vector field expressions and four plots displayed in a grid layout.
### Vector Field Expressions:
1. **\( F(x, y) = 5y\mathbf{i} \)**
2. **\( F(x, y) = 5y\mathbf{j} \)**
3. **\( F(x, y) = -5y\mathbf{i} \)**
4. **\( F(x, y) = -5y\mathbf{j} \)**
### Plots:
- Each plot shows a graph with vectors represented by red arrows. The vectors are scaled to avoid overlap.
#### Top Left Plot:
- **Vectors**: Horizontal in direction.
- **Description**: The vectors point rightward. The length of the vectors increases as the value of \( y \) increases positively.
#### Top Right Plot:
- **Vectors**: Vertical in direction.
- **Description**: The vectors point upward consistently. The length of the vectors increases as the value of \( y \) increases positively.
#### Bottom Left Plot:
- **Vectors**: Horizontal in direction.
- **Description**: The vectors point leftward. The length of the vectors increases as the value of \( y \) increases negatively.
#### Bottom Right Plot:
- **Vectors**: Vertical in direction.
- **Description**: The vectors point downward consistently. The length of the vectors increases as the value of \( y \) increases negatively.
The task requires matching the expressions with the correct plot based on the vector directions and magnitudes. The status at the bottom shows "Incorrect" indicating a mistake in the selections.
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