Explanation Given: Equation of curve is r ( t ) = 〈 cos t , sin t , 2 t 〉 Formula used: Velocity, v ( t ) = r ' ( t ) Acceleration, a ( t ) = r ' ' ( t ) Tangent vector , T = v ∥ v ∥ Normal vector, N = a N N a N , where a N = ∥ a N N ∥ , a N N = a − a T T and a T = a . T Binomial vector, B = T × N Calculation: We have v ( t ) = r ' ( t ) = 〈 − sin t , cos t , 2 〉 and a ( t ) = r ' ' ( t ) = 〈 − cos t , − sin t , 0 〉 We know, T = v ∥ v ∥ At t = π 2 , T = v ∥ v ∥ = 〈 1 , 0 , 2 〉 1 2 + 2 2 = 〈 1 5 , 0 , 2 5 〉 a T = a . T At t = π 2 , a T = a ... To determine Part b: Equation of oscillating plane at the point corresponding to t = π 2 for r ( t ) = 〈 cos t , sin t , 2 t 〉 ?

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14, Problem 38CRE

To determine

Part a:

T,N and B at the point corresponding to $t = \frac{π}{2}$ for $r (t) = 〈 \cos t, \sin t, 2 t 〉$ .

To determine

Part b:

Equation of oscillating plane at the point corresponding to $t = \frac{π}{2}$ for $r (t) = 〈 \cos t, \sin t, 2 t 〉$ ?

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Chapter 14, Problem 37CRE

Chapter 14, Problem 39CRE

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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Part a: T,N and B at the point corresponding to t = π 2 for r ( t ) = 〈 cos t , sin t , 2 t 〉 .

Solution Summary: The author explains how to determine T,N and B at the point corresponding to t = 2.

Concept explainers

Part a:

T,N and B at the point corresponding to $t = \frac{π}{2}$ for $r (t) = 〈 \cos t, \sin t, 2 t 〉$ .

Part b:

Equation of oscillating plane at the point corresponding to $t = \frac{π}{2}$ for $r (t) = 〈 \cos t, \sin t, 2 t 〉$ ?

Want to see the full answer?

Chapter 14 Solutions

Part a: T,N and B at the point corresponding to t = π 2 for r ( t ) = 〈 cos t , sin t , 2 t 〉 .

Solution Summary: The author explains how to determine T,N and B at the point corresponding to t = 2.

Concept explainers

Part a: T,N and B at the point corresponding to t=π2 for r(t)=〈cost,sint,2t〉.

Part b: Equation of oscillating plane at the point corresponding to t=π2 for r(t)=〈cost,sint,2t〉?

Want to see the full answer?

Chapter 14 Solutions

Part a:

T,N and B at the point corresponding to $t = \frac{π}{2}$ for $r (t) = 〈 \cos t, \sin t, 2 t 〉$ .

Part b:

Equation of oscillating plane at the point corresponding to $t = \frac{π}{2}$ for $r (t) = 〈 \cos t, \sin t, 2 t 〉$ ?