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1. F(г, у) (x+ y)i+ ( – y) j - 2. F(x, y) = (x – y) i+ (x + y)j - 3. F(x, у) yi+ cos x j 4. F(x, у) 2i+ xj 5. F(x, у) (2x + 2) i+ yj

1. F(г, у) (x+ y)i+ ( – y) j - 2. F(x, y) = (x – y) i+ (x + y)j - 3. F(x, у) yi+ cos x j 4. F(x, у) 2i+ xj 5. F(x, у) (2x + 2) i+ yj

Advanced Engineering Mathematics
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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Which vector field F has the graph? (image attached)

The image displays a vector field accompanied by several function options for \( \mathbf{F}(x, y) \). The vector field is illustrated on a Cartesian coordinate plane with axes labeled \( x \) and \( y \). The arrows represent the direction and magnitude of the vectors at different points in the plane. The vectors appear to spiral outward in a counter-clockwise direction, indicating a rotational component around the origin. The field's behavior suggests the presence of both radial and tangential vector components. Below the diagram, there are five vector function options labeled 1 through 5: 1. \( \mathbf{F}(x, y) = (x + y) \mathbf{i} + (x - y) \mathbf{j} \) 2. \( \mathbf{F}(x, y) = (x - y) \mathbf{i} + (x + y) \mathbf{j} \) 3. \( \mathbf{F}(x, y) = y \mathbf{i} + \cos x \mathbf{j} \) 4. \( \mathbf{F}(x, y) = 2 \mathbf{i} + x \mathbf{j} \) 5. \( \mathbf{F}(x, y) = (2x + 2) \mathbf{i} + y \mathbf{j} \) The task is to identify which of these functions corresponds to the displayed vector field.
Transcribed Image Text:The image displays a vector field accompanied by several function options for \( \mathbf{F}(x, y) \). The vector field is illustrated on a Cartesian coordinate plane with axes labeled \( x \) and \( y \). The arrows represent the direction and magnitude of the vectors at different points in the plane. The vectors appear to spiral outward in a counter-clockwise direction, indicating a rotational component around the origin. The field's behavior suggests the presence of both radial and tangential vector components. Below the diagram, there are five vector function options labeled 1 through 5: 1. \( \mathbf{F}(x, y) = (x + y) \mathbf{i} + (x - y) \mathbf{j} \) 2. \( \mathbf{F}(x, y) = (x - y) \mathbf{i} + (x + y) \mathbf{j} \) 3. \( \mathbf{F}(x, y) = y \mathbf{i} + \cos x \mathbf{j} \) 4. \( \mathbf{F}(x, y) = 2 \mathbf{i} + x \mathbf{j} \) 5. \( \mathbf{F}(x, y) = (2x + 2) \mathbf{i} + y \mathbf{j} \) The task is to identify which of these functions corresponds to the displayed vector field.
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