Explanation Given : r(t)= ( e t cos4t,e t sin4t ) Formula used: ∥ r'(t) ∥ = 2 + ( 4e t cos4t+e t sin4t ) 2 ? ( ( ? − 4 ? t s i n 4 t + ? t c o s 4 t ) ? 2 + ? ( 4 ? t c o s 4 t + ? t s i n 4 t ) ? 2 ) = a . b = ∥ a ∥ . ∥ b ∥ c o s θ Calculations: Compute the tangent vector, r ′ ( t ) r ′ ( t ) = ( -4e t sin4t+e t cos4t, 4e t cos4t+ e t sin4t ) r(t) .r' (t) = (e t cos4t,e t sin4t) .(-4e t sin4t+e t cos4t,4e t cos4t+e t sin4t) = -4e 2t cos4tsin4t+e 2t cos 2 4t+4e 2t sin4tcos4t+e 2t sin 2 4t = e 2t (cos 2 4t+sin 2 4t) = e 2t For computing norms, ∥ r(t) ∥ = e 2t sin 2 4t+e ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

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

Question

Chapter 14.2, Problem 65E

To determine

The angle ψ between the position vector and the tangent vector of Bernoulli spiral with parametrization as $r(t)= (e^{t} {cos4t,e}^{t} sin4t)$ constant.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.2, Problem 64E

Chapter 14.2, Problem 66E

Students have asked these similar questions

17. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.2.050. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) du 4√3- -4² Need Help? Read It SUBMIT ANSWER 18. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.2.051. Evaluate the integral. (Use C for the constant of integration.) - 49 dx x² +3 Need Help? Read It Watch It SUBMIT ANSWER 19. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.2.057. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 25+ x2 dx

Let (5,3,-7) and = (2, -3, -6). = Compute the following: u× u = -4(u xv) ux (-4v) (+v) × v=

Let a = (4, -2, -7) and 6 = (2,5, 3). (ã − ò) × (ã + b) =

Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The angle ψ between the position vector and the tangent vector of Bernoulli spiral with parametrization as r(t)= ( e t cos4t,e t sin4t ) constant.

Solution Summary: The author calculates the angle between the position vector and the tangent vector of the Bernoulli spiral with parametrization as r(t)= ( e t cos4t,e

Concept explainers

The angle ψ between the position vector and the tangent vector of Bernoulli spiral with parametrization as $r(t)= (e^{t} {cos4t,e}^{t} sin4t)$ constant.

Want to see the full answer?

Chapter 14 Solutions

The angle ψ between the position vector and the tangent vector of Bernoulli spiral with parametrization as r(t)= ( e t cos4t,e t sin4t ) constant.

Solution Summary: The author calculates the angle between the position vector and the tangent vector of the Bernoulli spiral with parametrization as r(t)= ( e t cos4t,e

Concept explainers

The angle ψ between the position vector and the tangent vector of Bernoulli spiral with parametrization as r(t)=(etcos4t,etsin4t) constant.

Want to see the full answer?

Chapter 14 Solutions

The angle ψ between the position vector and the tangent vector of Bernoulli spiral with parametrization as $r(t)= (e^{t} {cos4t,e}^{t} sin4t)$ constant.