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(d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove the following identities. (i) r" = s"T+ (s')²KN (ii) r′ × r″ = (s')³kB As a hint, start with the result from the lectures that r' =s'T and also that N=BxT.

(d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove the following identities. (i) r" = s"T+ (s')²KN (ii) r′ × r″ = (s')³kB As a hint, start with the result from the lectures that r' =s'T and also that N=BxT.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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(d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove the following identities. (i) r" = s"T+ (s')²KN (ii) r′ × r″ = (s')³kB As a hint, start with the result from the lectures that r' =s'T and also that N=BxT.
Transcribed Image Text:(d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove the following identities. (i) r" = s"T+ (s')²KN (ii) r′ × r″ = (s')³kB As a hint, start with the result from the lectures that r' =s'T and also that N=BxT.
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