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Let S₁ and S₂ be the spheres with equations x² + y² + z² - 2x +2y-2z+2 x² + y² + z² - 4x - 2y + 2z - 10 = 0 and = 0, respectively. a) Find the centres and radii of S₁ and $₂. b) Show¹ that the two spheres intersect in one single point and S₁ is contained in S₂. c) Do the two spheres intersect on the plane P = {(x, y, z) = R³ : x + 2y = 2z = 0}? Justify your answer.

Let S₁ and S₂ be the spheres with equations x² + y² + z² - 2x +2y-2z+2 x² + y² + z² - 4x - 2y + 2z - 10 = 0 and = 0, respectively. a) Find the centres and radii of S₁ and $₂. b) Show¹ that the two spheres intersect in one single point and S₁ is contained in S₂. c) Do the two spheres intersect on the plane P = {(x, y, z) = R³ : x + 2y = 2z = 0}? Justify your answer.

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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Let S₁ and S₂ be the spheres with equations x² + y² + z² - 2x +2y-2z+2 x² + y² + z² - 4x - 2y + 2z - 10 = 0 and = 0, respectively. a) Find the centres and radii of S₁ and S₂. b) Show¹ that the two spheres intersect in one single point and S₁ is contained in S₂. c) Do the two spheres intersect on the plane P = {(x, y, z) = R³ : x + 2y – 2z = 0}? Justify your answer.
Transcribed Image Text:Let S₁ and S₂ be the spheres with equations x² + y² + z² - 2x +2y-2z+2 x² + y² + z² - 4x - 2y + 2z - 10 = 0 and = 0, respectively. a) Find the centres and radii of S₁ and S₂. b) Show¹ that the two spheres intersect in one single point and S₁ is contained in S₂. c) Do the two spheres intersect on the plane P = {(x, y, z) = R³ : x + 2y – 2z = 0}? Justify your answer.
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