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(b) Show that cb (q-p).u≤|li|| dt. a

(b) Show that cb (q-p).u≤|li|| dt. a

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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Need help with part b). Please explain each step and neatly type up. Thank you :)

 

Question 5. In this problem we prove that a straight line is the shortest curve between two points in R". Let p, q € R" and let y be a curve such that y(a) = p, (b) = q, where a < b. (a) Show that, if u is a unit vector, then ·u ≤||||. (b) Show that (q − p) u≤ ≤ 11 |||| dt. (c) Show that the arc length of y from y(a) to y(b) is at least ||q - p||, with equality when y is a straight line.
Transcribed Image Text:Question 5. In this problem we prove that a straight line is the shortest curve between two points in R". Let p, q € R" and let y be a curve such that y(a) = p, (b) = q, where a < b. (a) Show that, if u is a unit vector, then ·u ≤||||. (b) Show that (q − p) u≤ ≤ 11 |||| dt. (c) Show that the arc length of y from y(a) to y(b) is at least ||q - p||, with equality when y is a straight line.
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