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Sketch the vector field. y 0 2 0 H 2 0 -2 0-2 2 -2 2 -2 2 -2 2 -2 F(x, y) = Y (22)

Sketch the vector field. y 0 2 0 H 2 0 -2 0-2 2 -2 2 -2 2 -2 2 -2 F(x, y) = Y (22)

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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**Sketch the Vector Field** This exercise involves sketching the vector field defined by the vector function \(\mathbf{F}(x, y) = \left\langle \frac{x}{2}, -\frac{y}{2} \right\rangle\). **Table of Points:** - \( (x, y) = (2, 0) \) - \( (x, y) = (0, 2) \) - \( (x, y) = (-2, 0) \) - \( (x, y) = (0, -2) \) - \( (x, y) = (2, 2) \) - \( (x, y) = (-2, -2) \) - \( (x, y) = (2, -2) \) - \( (x, y) = (-2, 2) \) Each row has a set of coordinates \( (x, y) \) and an empty box for calculating \(\mathbf{F}(x, y)\). **Graph Explanation:** Below the table is a Cartesian coordinate grid ranging from -5 to 5 on both the x and y axes. Users would sketch vectors originating from each point on the grid to represent the vector field. **Interactive Features:** - "Clear All" button to reset the drawing. - A "Draw" function, denoted by a pencil icon, allows users to draw vectors on the grid.
Transcribed Image Text:**Sketch the Vector Field** This exercise involves sketching the vector field defined by the vector function \(\mathbf{F}(x, y) = \left\langle \frac{x}{2}, -\frac{y}{2} \right\rangle\). **Table of Points:** - \( (x, y) = (2, 0) \) - \( (x, y) = (0, 2) \) - \( (x, y) = (-2, 0) \) - \( (x, y) = (0, -2) \) - \( (x, y) = (2, 2) \) - \( (x, y) = (-2, -2) \) - \( (x, y) = (2, -2) \) - \( (x, y) = (-2, 2) \) Each row has a set of coordinates \( (x, y) \) and an empty box for calculating \(\mathbf{F}(x, y)\). **Graph Explanation:** Below the table is a Cartesian coordinate grid ranging from -5 to 5 on both the x and y axes. Users would sketch vectors originating from each point on the grid to represent the vector field. **Interactive Features:** - "Clear All" button to reset the drawing. - A "Draw" function, denoted by a pencil icon, allows users to draw vectors on the grid.
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