Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let a(t) be a parametrized curve which does not pass through the origin. If a(to) is the point of the image of a closest to the origin and a' (to) 0, show that the position vector a(to) is orthogonal to a'(to). Let a be a regular space curve. Show that a(t) is a non-zero constant if and only if a(t) is orthogonal to a'(t) for all t € I.

Let a(t) be a parametrized curve which does not pass through the origin. If a(to) is the point of the image of a closest to the origin and a' (to) 0, show that the position vector a(to) is orthogonal to a'(to). Let a be a regular space curve. Show that a(t) is a non-zero constant if and only if a(t) is orthogonal to a'(t) for all t € I.

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
See similar textbooks
icon
Related questions
Question

Differential geometry 

Let a(t) be a parametrized curve which does not pass through the origin. If a(to) is the point of the image of a closest to the origin and a'(to) ‡ 0, show that the position vector a(to) is orthogonal to a'(to). Let a be a regular space curve. Show that a(t)| is a non-zero constant if and only if a(t) is orthogonal to a' (t) for all t = I.
Transcribed Image Text:Let a(t) be a parametrized curve which does not pass through the origin. If a(to) is the point of the image of a closest to the origin and a'(to) ‡ 0, show that the position vector a(to) is orthogonal to a'(to). Let a be a regular space curve. Show that a(t)| is a non-zero constant if and only if a(t) is orthogonal to a' (t) for all t = I.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS