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A smooth curve C is defined by some vector function R(t) with R (-) = (7,0,−2) and R′(t) = (2, √5 csc t, 2 cott) for all t € (0, π). ㅠ 1. Give a vector equation of the line tangent to C at the point where t = 2 2. Find the moving trihedral of C for all t € (0, π). 3. Reparametrize the unit tangent vector T(t) using the arc length as parameter starting from t = 1.

A smooth curve C is defined by some vector function R(t) with R (-) = (7,0,−2) and R′(t) = (2, √5 csc t, 2 cott) for all t € (0, π). ㅠ 1. Give a vector equation of the line tangent to C at the point where t = 2 2. Find the moving trihedral of C for all t € (0, π). 3. Reparametrize the unit tangent vector T(t) using the arc length as parameter starting from t = 1.

Algebra & Trigonometry with Analytic Geometry
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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A smooth curve C is defined by some vector function R(t) with R (-) = (7,0,−2) and R'(t) = (2, √5 csct, 2 cott) for all t ≤ (0, π). ㅠ 1. Give a vector equation of the line tangent to C at the point where t = 2 2. Find the moving trihedral of C for all t = (0, π). 3. Reparametrize the unit tangent vector T(t) using the arc length as parameter starting from t = 1.
Transcribed Image Text:A smooth curve C is defined by some vector function R(t) with R (-) = (7,0,−2) and R'(t) = (2, √5 csct, 2 cott) for all t ≤ (0, π). ㅠ 1. Give a vector equation of the line tangent to C at the point where t = 2 2. Find the moving trihedral of C for all t = (0, π). 3. Reparametrize the unit tangent vector T(t) using the arc length as parameter starting from t = 1.
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