**Match the Vector Field to the Corresponding Plot**1. $\langle 3, x \rangle$ [Input box]2. $\langle 3x + 3, y \rangle$ [Input box]3. $\langle y, \cos x \rangle$ [Input box]4. $\langle x + y, x - y \rangle$ [Input box](Enter A, B, C, or D)**Plots:**- **Plot A:** - Displays vectors on a two-dimensional plane with the x-axis and y-axis labeled. - Vectors appear as red arrows, pointing mostly horizontally and spaced evenly. - Magnitudes of vectors seem uniform across the plot.- **Plot B:** - Shows vectors on a two-dimensional plane with x-axis and y-axis labeled. - Vectors exhibit a spiral pattern, with direction changing gradually. - The density of the arrows appears higher near the origin, indicating a possible rotational component.Note: Plots C and D are not visible; only Plots A and B are described here. The image presents two vector field diagrams, labeled C and D.**Diagram C:** - The vector field consists of arrows pointing primarily in the horizontal direction, oriented from left to right.- The density and length of the arrows vary, indicating the magnitude and direction of the field.- The arrows are denser and longer as they move away from the y-axis, suggesting an increase in magnitude with distance from the center.- The plot covers the Cartesian plane from -6 to 6 on the y-axis and -4 to 4 on the x-axis.**Diagram D:**- This vector field shows horizontal arrows with a predominantly rightward direction across the entire plane.- The arrows are relatively uniform in length and density throughout the field.- Unlike Diagram C, the arrows are consistent in magnitude, showing a steadier field strength.- It also spans the Cartesian plane from -6 to 6 on the y-axis and -4 to 4 on the x-axis.Both diagrams are 2-dimensional representations in the Cartesian coordinate system, assisting in visualizing different types of vector fields commonly studied in physics and mathematics.

using online vector field graphing we get 1-A 2-C

Answered: 1. (3, x) 2. (3x + 3, y) 3. (y, cos x)…

Math

Advanced Math

1. (3, x) 2. (3x + 3, y) 3. (y, cos x) 4. (x + y, x – Y)

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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