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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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