Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
a. Show that n(t) = -g'(t)i + f(t)j and - n(t)=g'(t)i-f'(t)j are both normal to the curve r(t) = f(t)i + g(t)j at the point (f(t).g(t)). To obtain N for a particular plane curve, choose the one of n or -n that points toward the concave side of the curve, and make it into a unit vector. (See the figure to the right.) Apply this method to find N for the following curves. b. r(t) = 6ti +6e¹j 6 c. r(t) = √/36-251² i +5tj.-st N-14 N-14 The vector dT/ds, normal to the curve, always points in the direction in which T is turning. The unit normal vector N is the direction of dT/ds.

a. Show that n(t) = -g'(t)i + f(t)j and - n(t)=g'(t)i-f'(t)j are both normal to the curve r(t) = f(t)i + g(t)j at the point (f(t).g(t)). To obtain N for a particular plane curve, choose the one of n or -n that points toward the concave side of the curve, and make it into a unit vector. (See the figure to the right.) Apply this method to find N for the following curves. b. r(t) = 6ti +6e¹j 6 c. r(t) = √/36-251² i +5tj.-st N-14 N-14 The vector dT/ds, normal to the curve, always points in the direction in which T is turning. The unit normal vector N is the direction of dT/ds.

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
a. Show that n(t) = -g'(t)i + f'(t)j and - n(t) = g'(t)i-f'(t)j are both normal to the curve r(t) = f(t)i + g(t)j at the point (f(t),g(t)). To obtain N for a particular plane curve, choose the one of n or -n that points toward the concave side of the curve, and make it into a unit vector. (See the figure to the right.) Apply this method to find N for the following curves. b. r(t) = 6ti +6e¹j 6 c. r(t) = √36 - 25t² i + 5tj, -st≤ 14T sk N-14T Kds The vector dT/ds, normal to the curve, always points in the direction in which T is turning. The unit normal vector N is the direction of dT/ds.
Transcribed Image Text:a. Show that n(t) = -g'(t)i + f'(t)j and - n(t) = g'(t)i-f'(t)j are both normal to the curve r(t) = f(t)i + g(t)j at the point (f(t),g(t)). To obtain N for a particular plane curve, choose the one of n or -n that points toward the concave side of the curve, and make it into a unit vector. (See the figure to the right.) Apply this method to find N for the following curves. b. r(t) = 6ti +6e¹j 6 c. r(t) = √36 - 25t² i + 5tj, -st≤ 14T sk N-14T Kds The vector dT/ds, normal to the curve, always points in the direction in which T is turning. The unit normal vector N is the direction of dT/ds.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 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