Answered: Outward normal to a sphere Show that |…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 53E

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Question

Outward normal to a sphere Show that | t_u x t_v | = a² sin u for a sphere of radius a defined parametrically by r(u, v) = ⟨a sin u cos v, a sin u sin v, a cos u⟩ , where 0 ≤ u ≤ π and 0 ≤ v ≤ 2π.

Expert Solution

Step 1

Given: $r (u, v) = <a \sin u \cos v, a \sin u \sin v, a \cos u>$

To show: $|t_{u} \times t_{v}| = a^{2} \sin u$

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