Needed to be solved part b compelete correclty in 30 minutes and get the thumbs up please show neat and clean work. Please by hand solution is needed b) For a general curve r: 1R, define the vectors t(s), n(s) and b(s) asr(s)t(s)t'(s)n(s)and b(s) = t(s) x n(x).You may assume r(s) and ||t'(s)|| are non-zero.i) Prove b(s) has unit length and hence prove b'(s) is perpendicular to b(s).i) Deduce veclors t(s), n(s) and b(s) are an orthogonal basis.iii) Hence or otherwise prove b'(s) is parallel to n(s).

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b) For a general curve r: 1R, define the vectors t(s), n(s) and b(s) as t(s) - r(s) (s) and b(s) = t(s) x n(x). n(s) You may assunne ||r(s)|| and U(s) are non-zero. i) Prove b(s) has unit length and hence prove b'(s) is perpendicular to b(s). i) Deduce veclors t(s), n(s) and b(s) are an orthogonal basis. iii) Hence or otherwise prove b'(s) is parallel to n(s).

b) For a general curve r: 1R, define the vectors t(s), n(s) and b(s) as t(s) - r(s) (s) and b(s) = t(s) x n(x). n(s) You may assunne ||r(s)|| and U(s) are non-zero. i) Prove b(s) has unit length and hence prove b'(s) is perpendicular to b(s). i) Deduce veclors t(s), n(s) and b(s) are an orthogonal basis. iii) Hence or otherwise prove b'(s) is parallel to n(s).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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