Let y: R→ R³ be a unit speed curve. Let T, N, B denote the Frenet frame of y, and let K, T denote the curvature and torsion of y respectively. Further, suppose the curvature x(t) satisfies x(t) #0 for all t. Define another curve : R → R³ by B(t) = It can be shown that (1) f(t) N for some function f(t). What is f(t)? Select one: O a. 0 O b. 1 O c. t O d. O e. k(t) O f. -k(t) O g. r(t) Oh. -t(t) Oi. K(t)² Ο j. τ(t)2 Ok. K(t)t(t) -t dy(t) dt .
Let y: R→ R³ be a unit speed curve. Let T, N, B denote the Frenet frame of y, and let K, T denote the curvature and torsion of y respectively. Further, suppose the curvature x(t) satisfies x(t) #0 for all t. Define another curve : R → R³ by B(t) = It can be shown that (1) f(t) N for some function f(t). What is f(t)? Select one: O a. 0 O b. 1 O c. t O d. O e. k(t) O f. -k(t) O g. r(t) Oh. -t(t) Oi. K(t)² Ο j. τ(t)2 Ok. K(t)t(t) -t dy(t) dt .
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:Let y: R → R³ be a unit speed curve. Let T, N, B denote the Frenet frame of y, and let K, T denote the curvature and torsion of y respectively.
Further, suppose the curvature (t) satisfies k(t) ‡ 0 for all t. Define another curve ß: R → R³ by
It can be shown that (t) = f(t)N for some function f(t). What is f(t)?
Select one:
O a. 0
O b. 1
O c. t
d. -t
O e. k(t)
f. -k(t)
g. t(t)
Oh. -t(t)
○i. K(t)²
τ(t)2
K(t)t(t)
B(t) =
Ο j.
Ok.
dy(t)
dt
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