(5) Consider the plane defined by x+y+z+5= 0. Let (ro, Yo, zo) be an arbitrary point in R³ and let (2*, y, z) be the point in the plane that is closest to (zo. yo. 2o). (a) Using optimization, show that the distance D between (ro, yo, 2o) and (x, y, z) is given by co + yo +20 + 51 D(10:30, 20) (b) Using the above, compute the minimum distance between the plane and the curve defined by x² + y² = 2; 2 = 0.
(5) Consider the plane defined by x+y+z+5= 0. Let (ro, Yo, zo) be an arbitrary point in R³ and let (2*, y, z) be the point in the plane that is closest to (zo. yo. 2o). (a) Using optimization, show that the distance D between (ro, yo, 2o) and (x, y, z) is given by co + yo +20 + 51 D(10:30, 20) (b) Using the above, compute the minimum distance between the plane and the curve defined by x² + y² = 2; 2 = 0.
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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