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(3) Consider the surface of revolution H = {(x, y, z) € R³ | x² + z² = (² + cos³½)²)}. (a) Find the tangent plane to H at (2/2)) 3 π, 2√2 (See also (Q7) of Problem Sheet 7.) (b) Find the unit normals to H at (23/2,π, 2√2 3 2√2 (c) Which of the two unit normals in (b) represents the "outward-facing" side of H? (For part (c), you do not have to prove the answer. You can find the answer by sketching H and the appropriate normals and then inspecting your sketch.)

(3) Consider the surface of revolution H = {(x, y, z) € R³ | x² + z² = (² + cos³½)²)}. (a) Find the tangent plane to H at (2/2)) 3 π, 2√2 (See also (Q7) of Problem Sheet 7.) (b) Find the unit normals to H at (23/2,π, 2√2 3 2√2 (c) Which of the two unit normals in (b) represents the "outward-facing" side of H? (For part (c), you do not have to prove the answer. You can find the answer by sketching H and the appropriate normals and then inspecting your sketch.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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(3) Consider the surface of revolution H = {(x, y, z) € R³ | x² + z² = (² + cos³½)²)}. (a) Find the tangent plane to H at (2/2)) 3 π, 2√2 (See also (Q7) of Problem Sheet 7.) (b) Find the unit normals to H at (23/2,π, 2√2 3 2√2 (c) Which of the two unit normals in (b) represents the "outward-facing" side of H? (For part (c), you do not have to prove the answer. You can find the answer by sketching H and the appropriate normals and then inspecting your sketch.)
Transcribed Image Text:(3) Consider the surface of revolution H = {(x, y, z) € R³ | x² + z² = (² + cos³½)²)}. (a) Find the tangent plane to H at (2/2)) 3 π, 2√2 (See also (Q7) of Problem Sheet 7.) (b) Find the unit normals to H at (23/2,π, 2√2 3 2√2 (c) Which of the two unit normals in (b) represents the "outward-facing" side of H? (For part (c), you do not have to prove the answer. You can find the answer by sketching H and the appropriate normals and then inspecting your sketch.)
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