Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![1. **(Section 17.1)** Match the vector fields with their sketches below by placing the letter of the function in the corresponding blank:
\[
\begin{array}{lll}
\text{(I)} & \vec{F}(x, y) = \langle -y, -x \rangle & \\
\text{(II)} & \vec{F}(x, y) = \langle y^2, x \rangle & \\
\text{(III)} & \vec{F}(x, y) = \langle y, -x \rangle & \\
\text{(IV)} & \vec{F}(x, y) = \langle x + y, y - x \rangle & \\
\end{array}
\]
- **Vector Field (A):**
- **Vector Field (B):**
- **Vector Field (C):**
- **Vector Field (D):**
### Explanation of Vector Field Diagrams
**Vector Field (A):**
- The arrows form concentric circular patterns around the origin, indicating a spiral or rotational field.
**Vector Field (B):**
- The arrows are directed outward from the center, suggesting a divergence from the origin.
**Vector Field (C):**
- The vectors appear to create a clockwise circular motion around the origin, potentially indicative of a curl or vortex.
**Vector Field (D):**
- The pattern shows arrows converging towards the center, suggesting an inward flow to the origin.](https://content.bartleby.com/qna-images/question/251f9165-68ff-4948-bb45-e4b672f91d1b/c5ff6e4e-7b8e-46ad-8909-3e955bd30f84/licif3_processed.png)
Transcribed Image Text:1. **(Section 17.1)** Match the vector fields with their sketches below by placing the letter of the function in the corresponding blank:
\[
\begin{array}{lll}
\text{(I)} & \vec{F}(x, y) = \langle -y, -x \rangle & \\
\text{(II)} & \vec{F}(x, y) = \langle y^2, x \rangle & \\
\text{(III)} & \vec{F}(x, y) = \langle y, -x \rangle & \\
\text{(IV)} & \vec{F}(x, y) = \langle x + y, y - x \rangle & \\
\end{array}
\]
- **Vector Field (A):**
- **Vector Field (B):**
- **Vector Field (C):**
- **Vector Field (D):**
### Explanation of Vector Field Diagrams
**Vector Field (A):**
- The arrows form concentric circular patterns around the origin, indicating a spiral or rotational field.
**Vector Field (B):**
- The arrows are directed outward from the center, suggesting a divergence from the origin.
**Vector Field (C):**
- The vectors appear to create a clockwise circular motion around the origin, potentially indicative of a curl or vortex.
**Vector Field (D):**
- The pattern shows arrows converging towards the center, suggesting an inward flow to the origin.
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