Let S be the surface in R° parameterized by r(u, v) = (v cos(u), v, v sin(u)), for 0 < u < 2n and 0 < v < 2.(a) Select the surface S below.Z(b) Choose the correct ru X r, of the given parameterization r(u, v).O ru × ry = (-v cos(u), v, –v sin(u))

Answered: Let S be the surface in R°…

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 S be the surface in R° parameterized by r(u, v) = (v cos(u), v, v sin(u)), for 0 < u < 2n and 0 < v < 2.
(a) Select the surface S below.
Z
(b) Choose the correct ru X r, of the given parameterization r(u, v).
O ru × ry = (-v cos(u), v, –v sin(u))

Expert Solution

Step 1

Given,

$r (u, v) = <v \cos u, v, v \sin u> \Rightarrow x = v \cos u, y = v, z = v \sin u \Rightarrow x^{2} + z^{2} = v^{2} \Rightarrow x^{2} + z^{2} = y^{2}$

this is an equation of cone whose axis is along y-axis

hence ,the selection is $(1)$

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