Answered: and v ∈ [1, 3], which describes the…

and v ∈ [1, 3], which describes the surface S represented in the following graph: image1 A normal vector to the surface S, with the orientation given in the previous graph, corresponds to: image 2

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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Question

Consider the parametrization r (u, v) = (v, 2 cos u, 4 sin u), with u ∈ [ 0 , π/2]
and v ∈ [1, 3], which describes the surface S represented in the following graph:

image1

A normal vector to the surface S, with the orientation given in the previous graph, corresponds to:

image 2

A) N = (0, –2 sin u, 4 cos u)
B) N = (0,4 cos u, 2 sin u)
C) N = (0, -4cos u, -2 sin u)
D) N = (1,0,0)

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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