Explanation Given: Equation of the curve in vector form is r ( θ ) = 〈 sin θ , cos θ , cos 3 θ 〉 , θ = π 3 Calculation: We have r ( θ ) = 〈 sin θ , cos θ , cos 3 θ 〉 ð Velocity, v ( θ ) = r ' ( θ ) = 〈 cos θ , − sin θ , − 3 sin 3 θ 〉 , v ( π 3 ) = 〈 1 2 , − 3 2 , 0 〉 ð Acceleration, a ( θ

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 14.5, Problem 5E

To determine

The velocity and acceleration vectors and the speed for $r (θ) = 〈 \sin θ, \cos θ, \cos 3 θ 〉, θ = \frac{π}{3}$ .

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Chapter 14.5, Problem 4E

Chapter 14.5, Problem 6E

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Chapter 14 Solutions

Calculus - Standalone book

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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The velocity and acceleration vectors and the speed for r ( θ ) = 〈 sin θ , cos θ , cos 3 θ 〉 , θ = π 3 .

Solution Summary: The author explains how the velocity and acceleration vectors and the speed for r ( ) ='sin', cos, and co 3 are found out.

Concept explainers

The velocity and acceleration vectors and the speed for $r (θ) = 〈 \sin θ, \cos θ, \cos 3 θ 〉, θ = \frac{π}{3}$ .

Want to see the full answer?

Chapter 14 Solutions

The velocity and acceleration vectors and the speed for r ( θ ) = 〈 sin θ , cos θ , cos 3 θ 〉 , θ = π 3 .

Solution Summary: The author explains how the velocity and acceleration vectors and the speed for r ( ) ='sin', cos, and co 3 are found out.

Concept explainers

The velocity and acceleration vectors and the speed for r(θ)=〈sinθ,cosθ,cos3θ〉,θ=π3.

Want to see the full answer?

Chapter 14 Solutions

The velocity and acceleration vectors and the speed for $r (θ) = 〈 \sin θ, \cos θ, \cos 3 θ 〉, θ = \frac{π}{3}$ .