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Consider the vector function given below. r(t) = (5t, 3 cos(t), 3 sin(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). (5,-3 sin(t),3 cos (t)) √34 T(t) N(t) 0, (b) Use the formula x(t) k(t) = √2 =cos (t), - /34 3 √17 IT'(t)| Ir' (t)\ 3 sin(t) √34 X to find the curvature.

Consider the vector function given below. r(t) = (5t, 3 cos(t), 3 sin(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). (5,-3 sin(t),3 cos (t)) √34 T(t) N(t) 0, (b) Use the formula x(t) k(t) = √2 =cos (t), - /34 3 √17 IT'(t)| Ir' (t)\ 3 sin(t) √34 X to find the curvature.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 6E
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Consider the vector function given below. r(t) = (5t, 3 cos(t), 3 sin(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). (5,-3 sin (t),3 cos (t)) √34 T(t) = N(t) = 0, 3 √34 (b) Use the formula x(t) x(t) = √2 cos (t), - 3 √17 IT'(t)| Ir' (t) X 3 sin(t) √34 X to find the curvature.
Transcribed Image Text:Consider the vector function given below. r(t) = (5t, 3 cos(t), 3 sin(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). (5,-3 sin (t),3 cos (t)) √34 T(t) = N(t) = 0, 3 √34 (b) Use the formula x(t) x(t) = √2 cos (t), - 3 √17 IT'(t)| Ir' (t) X 3 sin(t) √34 X to find the curvature.
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