20. Let S be an oriented surface parametrized by r(u,v). Define the notation do = r, du × r, dv so that do is a vector normal to the surface. Also, the magnitude do = face area (by Equation 5 in Section 16.5). Derive the identity do is the element of sur- do = (EG – F²)'/² du dv where E = r?, F = r„ • r,, and G = |r,|?.

20. Let S be an oriented surface parametrized by r(u,v). Define the notation do = r, du × r, dv so that do is a vector normal to the surface. Also, the magnitude do = face area (by Equation 5 in Section 16.5). Derive the identity do is the element of sur- do = (EG – F²)'/² du dv where E = r?, F = r„ • r,, and G = |r,|?.

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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