Find a unit vector u that is normal to the level curve of f(x, y) = 5x²y through P = (x, y) = (5,-4) at P.
Find a unit vector u that is normal to the level curve of f(x, y) = 5x²y through P = (x, y) = (5,-4) at P.
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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Question
![**Title: Finding a Unit Vector Normal to a Level Curve**
**Objective:**
Determine a unit vector **u** that is normal to the level curve of \( f(x, y) = 5x^2 y \) through \( P = (x, y) = (5, -4) \) at \( P \).
**Graph Explanation:**
The figure shows the level curves of \( f(x, y) = ax^2 y \). The graph is centered at the origin (0, 0) with the x-axis and y-axis marked. The curves are symmetric about both the x-axis and y-axis and resemble a hyperbolic pattern. Positive and negative values of \( a \) are showcased, depicting how the constant \( a \) affects the steepness and direction of the curves.
**Task:**
Give your answer using component form or standard basis vectors. Express numbers in exact form, using symbolic notation and fractions where needed.
**Prompt:**
\[ \mathbf{u} = \] [Text Box for Answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F609cd648-ee60-4e65-94f5-e2f0e2671842%2F804c937d-66d0-4950-8f2d-007b69d13f4e%2Fplwvgq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Finding a Unit Vector Normal to a Level Curve**
**Objective:**
Determine a unit vector **u** that is normal to the level curve of \( f(x, y) = 5x^2 y \) through \( P = (x, y) = (5, -4) \) at \( P \).
**Graph Explanation:**
The figure shows the level curves of \( f(x, y) = ax^2 y \). The graph is centered at the origin (0, 0) with the x-axis and y-axis marked. The curves are symmetric about both the x-axis and y-axis and resemble a hyperbolic pattern. Positive and negative values of \( a \) are showcased, depicting how the constant \( a \) affects the steepness and direction of the curves.
**Task:**
Give your answer using component form or standard basis vectors. Express numbers in exact form, using symbolic notation and fractions where needed.
**Prompt:**
\[ \mathbf{u} = \] [Text Box for Answer]
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