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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
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

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.
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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