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a) The equation of the unit sphere of three-dimensional space is X²+Y²+Z² = 1. The variables are stretched by coefficients a, b and c: x = aX, y = bY and z = cZ. What is the relationship between the new variables x, y and z? What is the name of this surface? b) Form the parametrization of the surface at point a by stretching the parametrization of the sphere in a suitable way. c) Determine the surface related to the previous points 3x² + 4y² + 5z² = 33 normal vector at a point (2, -2, 1).

a) The equation of the unit sphere of three-dimensional space is X²+Y²+Z² = 1. The variables are stretched by coefficients a, b and c: x = aX, y = bY and z = cZ. What is the relationship between the new variables x, y and z? What is the name of this surface? b) Form the parametrization of the surface at point a by stretching the parametrization of the sphere in a suitable way. c) Determine the surface related to the previous points 3x² + 4y² + 5z² = 33 normal vector at a point (2, -2, 1).

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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a) The equation of the unit sphere of three-dimensional space is X²+Y²+Z² = 1. The variables are stretched by coefficients a, b and c: x = ax, y = bY and z = cZ. What is the relationship between the new variables x, y and z? What is the name of this surface? b) Form the parametrization of the surface at point a by stretching the parametrization of the sphere in a suitable way. c) Determine the surface related to the previous points 3x² + 4y² + 5z² = 33 normal vector at a point (2, −2, 1).
Transcribed Image Text:a) The equation of the unit sphere of three-dimensional space is X²+Y²+Z² = 1. The variables are stretched by coefficients a, b and c: x = ax, y = bY and z = cZ. What is the relationship between the new variables x, y and z? What is the name of this surface? b) Form the parametrization of the surface at point a by stretching the parametrization of the sphere in a suitable way. c) Determine the surface related to the previous points 3x² + 4y² + 5z² = 33 normal vector at a point (2, −2, 1).
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