Homework Help is Here – Start Your Trial Now!
Math
Calculus
Find B and t for the space curve r(t) = (5 sin t) i + (5 cos t) j+(12t) k. 5 cos ti+ 13 5 sin 13 12 T = j+ k 13 25 N = (- sin t) i + ( – cos t) j The binormal vector is B = j+ (O k. i+ The torsion is t = (Type an integer or a simplified fraction.)

Find B and t for the space curve r(t) = (5 sin t) i + (5 cos t) j+(12t) k. 5 cos ti+ 13 5 sin 13 12 T = j+ k 13 25 N = (- sin t) i + ( – cos t) j The binormal vector is B = j+ (O k. i+ The torsion is t = (Type an integer or a simplified fraction.)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
100%
25 Plz explain in detail what torsion is and what formula to use for it. Plz also solve the problem I have attached an example
Find B and t for the space curve rit) = (3 cos t) i• (3 sin t)j (4t) k. N = (- cos t) i+(-sin t)j B, the binormal vector, is defined as TXN. B-TN- sint cost - cost - sint 0 Write the determinant using three subdeterminants and evaluate each one. B- cost ant cos - cost o - cost -sint Evaluate the determinant for the i-component. - sin t) =sin t - sint o Evaluate the determinant for the jcomponent - cos t) cos t Evaluate the determinant for the k-component. Use the idertity sint + cos1=1 to simplity the result. - sin t) - cos )(- cos t) cost -sint Thus, the binomal vector is B The definition for the torsion, t, is shown below. |vxa Examp o httpsndtemprod pearsonomg comapivprintimath 2/12021 Secton 135 Enhanced AssigmentKaya Brulotta Differentiate r() - 3 cos t) i+ (3 sin t) j (41) k to get the velocity vector. v(t) =(-3 sin t) i+ (3 cos t) j+ (4) k Differentiate v) (-3 sin 1) i+ (3 cos 1)j+(4) k to get the acceleration vector. a(t) =(-3 cos t) i+(-3 sin t)j+ (0) k confurcdr Differentiate at) =(-3 cos t) i+(-3 sin 1)j+ (0) k to get the final row for the matrix. a') = (3 sin t)i+(-3 cos t)j• (0) k Write the determinant for the numerator of the torsion using the three previous results. -3 sint 3 cost 4 -3 cost -3 sint 0 3 sint -3 cost o Write the determinant using three subdeterminants. For this case, two of the subdeterminants are zero. -3 sint 3 cost 4 -3 cost -3 sin t -3 cost 3 sint -3 cost -3 sint 0 -3 cost 0 Evaluate the remaining determinant. Use the identity sint + cos1-1 to simplity the result 3 cost -3 sint 3 sint -3 cost 4(-3 cos 1X-3 cos t)-(-3 sin t)3 sin - 36( sin 1+ cos ) 36 The denominator from the definition for torsion is vxa. Evaluate the cross product. -3 sint 3 cost 4 Vxa -3 cost -3 sint 0 Write the determinant using three subdeterminants and evaluate each one. 3 cost 4. -3 sint 4 -3 cost (12 sin t) i(- 12 cos t) + (9) k -3 sint 3 cos t. -3 cost -3 sin t -3 sint 0 Evaluate |vxa. where vxa (12 sin t)i+(-12 cos 1)j+ (9) k. vxa= (12 sin 1 + (- 12 cos t + (9) = 225 Combine the results for the numerator and the denominator, 36 and 225, and simplify to find the torsion. 225 25
Transcribed Image Text:Find B and t for the space curve rit) = (3 cos t) i• (3 sin t)j (4t) k. N = (- cos t) i+(-sin t)j B, the binormal vector, is defined as TXN. B-TN- sint cost - cost - sint 0 Write the determinant using three subdeterminants and evaluate each one. B- cost ant cos - cost o - cost -sint Evaluate the determinant for the i-component. - sin t) =sin t - sint o Evaluate the determinant for the jcomponent - cos t) cos t Evaluate the determinant for the k-component. Use the idertity sint + cos1=1 to simplity the result. - sin t) - cos )(- cos t) cost -sint Thus, the binomal vector is B The definition for the torsion, t, is shown below. |vxa Examp o httpsndtemprod pearsonomg comapivprintimath 2/12021 Secton 135 Enhanced AssigmentKaya Brulotta Differentiate r() - 3 cos t) i+ (3 sin t) j (41) k to get the velocity vector. v(t) =(-3 sin t) i+ (3 cos t) j+ (4) k Differentiate v) (-3 sin 1) i+ (3 cos 1)j+(4) k to get the acceleration vector. a(t) =(-3 cos t) i+(-3 sin t)j+ (0) k confurcdr Differentiate at) =(-3 cos t) i+(-3 sin 1)j+ (0) k to get the final row for the matrix. a') = (3 sin t)i+(-3 cos t)j• (0) k Write the determinant for the numerator of the torsion using the three previous results. -3 sint 3 cost 4 -3 cost -3 sint 0 3 sint -3 cost o Write the determinant using three subdeterminants. For this case, two of the subdeterminants are zero. -3 sint 3 cost 4 -3 cost -3 sin t -3 cost 3 sint -3 cost -3 sint 0 -3 cost 0 Evaluate the remaining determinant. Use the identity sint + cos1-1 to simplity the result 3 cost -3 sint 3 sint -3 cost 4(-3 cos 1X-3 cos t)-(-3 sin t)3 sin - 36( sin 1+ cos ) 36 The denominator from the definition for torsion is vxa. Evaluate the cross product. -3 sint 3 cost 4 Vxa -3 cost -3 sint 0 Write the determinant using three subdeterminants and evaluate each one. 3 cost 4. -3 sint 4 -3 cost (12 sin t) i(- 12 cos t) + (9) k -3 sint 3 cos t. -3 cost -3 sin t -3 sint 0 Evaluate |vxa. where vxa (12 sin t)i+(-12 cos 1)j+ (9) k. vxa= (12 sin 1 + (- 12 cos t + (9) = 225 Combine the results for the numerator and the denominator, 36 and 225, and simplify to find the torsion. 225 25
Find B and t for the space curve r(t) = (5 sin t) i+ (5 cos t) j+ (12t) k. 12 T = -cos 13 i+ sin t j+ k 13 13 25 N = (- sin t) i + (- cos t) j The binormal vector is B = i+ i+ k. The torsion is t = (Type an integer or a simplified fraction.)
Transcribed Image Text:Find B and t for the space curve r(t) = (5 sin t) i+ (5 cos t) j+ (12t) k. 12 T = -cos 13 i+ sin t j+ k 13 13 25 N = (- sin t) i + (- cos t) j The binormal vector is B = i+ i+ k. The torsion is t = (Type an integer or a simplified fraction.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Inequality
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.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS