8. Given the space curve C as the image of the vector valued function r(t) = 2ti+t³j+-t-¹ k OR r(t) = (cos(t), sin(t), t) compute both the unit normal vector T(t) and the unit normal vector N(t). Furthermore, use the formula T'(t)| _ \r'(t) ×r"(t)| r' (t) ³ r(t) to compute its curvature. K=

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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8. Given the space curve C as the image of the vector valued function
OR
r(t) = 2ti+t³j+-t-¹ k
3
r(t) = (cos(t), sin(t), t)
compute both the unit normal vector T(t) and the unit normal vector N(t). Furthermore, use the formula
T'(t)| __ \r' (t) × r"(t)|
r' (t) ³
=
r' (t)
to compute its curvature.
K=
Transcribed Image Text:8. Given the space curve C as the image of the vector valued function OR r(t) = 2ti+t³j+-t-¹ k 3 r(t) = (cos(t), sin(t), t) compute both the unit normal vector T(t) and the unit normal vector N(t). Furthermore, use the formula T'(t)| __ \r' (t) × r"(t)| r' (t) ³ = r' (t) to compute its curvature. K=
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