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Consider the function or defined by o(u, v) (sin u cos v, sin u sin v, cos u). - Suppose now that or is defined on a domain such that it becomes a regular surface patch for the unit sphere S². Which of the following describes a unit normal vector field N on S² ? Select one: O a. N(x, y, z) = (0,0,1) O b. N(x, y, z) = (x, y, z) Oc. N(x, y, z)=(x, y, z) - Od. N(o(u, v)) = (u, v) Oe. N(o(u, v)) = (u, v, 0) Of. N(o(u, v)) = (cos u cos v, cos u sin v, sin u)

Consider the function or defined by o(u, v) (sin u cos v, sin u sin v, cos u). - Suppose now that or is defined on a domain such that it becomes a regular surface patch for the unit sphere S². Which of the following describes a unit normal vector field N on S² ? Select one: O a. N(x, y, z) = (0,0,1) O b. N(x, y, z) = (x, y, z) Oc. N(x, y, z)=(x, y, z) - Od. N(o(u, v)) = (u, v) Oe. N(o(u, v)) = (u, v, 0) Of. N(o(u, v)) = (cos u cos v, cos u sin v, sin u)

Advanced Engineering Mathematics
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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Consider the function o defined by o(u, v) = (sin u cos v, sin u sin v, cos u). Suppose now that o is defined on a domain such that it becomes a regular surface patch for the unit sphere S². Which of the following describes a unit normal vector field N on S2 ? Select one: Who I O a. N(x, y, z) = (0,0,1) Ob. N(x, y, z) = (x, y, z) Oc. N(x, y, z)=(x, y, z) Od. N(o(u, v)) = (u, v) Oe. N(o(u, v)) = (u, v, 0) Of N(o(u, v)) = (cos u cos v, cos u sin v, sin u)
Transcribed Image Text:Consider the function o defined by o(u, v) = (sin u cos v, sin u sin v, cos u). Suppose now that o is defined on a domain such that it becomes a regular surface patch for the unit sphere S². Which of the following describes a unit normal vector field N on S2 ? Select one: Who I O a. N(x, y, z) = (0,0,1) Ob. N(x, y, z) = (x, y, z) Oc. N(x, y, z)=(x, y, z) Od. N(o(u, v)) = (u, v) Oe. N(o(u, v)) = (u, v, 0) Of N(o(u, v)) = (cos u cos v, cos u sin v, sin u)
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