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Consider the ellipsoid 4x2 + 36y2 + 225 z2 = 225 (a) Parametrize the surface S = r(u, v) by x = a sin(u) sin(v), y = b cos(u) sin(v), and z = c cos(v) with appropriate values for a, b and c. (b) Determine the unit normal vector n for the point π 4 , π 4  in (u, v) space

Consider the ellipsoid 4x2 + 36y2 + 225 z2 = 225 (a) Parametrize the surface S = r(u, v) by x = a sin(u) sin(v), y = b cos(u) sin(v), and z = c cos(v) with appropriate values for a, b and c. (b) Determine the unit normal vector n for the point π 4 , π 4  in (u, v) space

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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1. Consider the ellipsoid 4x2 + 36y2 + 225 z2 = 225

(a) Parametrize the surface S = r(u, v) by x = a sin(u) sin(v), y = b cos(u) sin(v), and z = c cos(v) with appropriate values for a, b and c.

(b) Determine the unit normal vector n for the point π 4 , π 4  in (u, v) space. (c) Evaluate directly ZZ S F · dS where F = 2y2i -6z2j +15k 

1. Consider the ellipsoid a?a² + B?y? + v²z² = y? a sin(u) sin(v), y = b and c. b cos(u) sin(v), (a) Parametrize the surface S = r(u, v) by x = and z = c cos(v) with appropriate values for а, (b) Determine the unit normal vector n for the point ( ) in (u, v) space. 4’4 Evaluate directly || F. dS where F = ay?i – Bz²j+yk
Transcribed Image Text:1. Consider the ellipsoid a?a² + B?y? + v²z² = y? a sin(u) sin(v), y = b and c. b cos(u) sin(v), (a) Parametrize the surface S = r(u, v) by x = and z = c cos(v) with appropriate values for а, (b) Determine the unit normal vector n for the point ( ) in (u, v) space. 4’4 Evaluate directly || F. dS where F = ay?i – Bz²j+yk
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