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) = 7ti+5e'j c. r(t) = -√4-811³i+9tj. - sts c. N= +49 (vzde +ay) (120€ +49) √√4-8112 2 i+ N2 4 N-14, N-10 The vector dT/ds, normal to the curve, always points in the direction in which Tis 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) = 7ti+5e'j c. r(t) = -√4-811³i+9tj. - sts c. N= +49 (vzde +ay) (120€ +49) √√4-8112 2 i+ N2 4 N-14, N-10 The vector dT/ds, normal to the curve, always points in the direction in which Tis 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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Pls do part C, thw answer shown is wrong
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) = 7ti+5e¹j
c. r(t) = √4-811² i +9tj,-sts
c. N=
120e +4y
√√4-811²
2
2
J (√25e J
+43
9t
4
27
***
N-
14T
di
N-14
Pot
The vector dT/ds, normal to the curve,
always points in the direction in which Tis
turning. The unit normal vector N is the
direction of dT/ds.
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