Explanation Given information: The vector valued function r ( t ) is, r ( t ) = ( 2 i + 2 j + k ) + cos t ( 1 2 i − 1 2 j ) + sin t ( 1 3 i + 1 3 j + 1 3 k ) (1) Equation of the plane is, x + y − 2 z = 2 (2) Calculation: From equation (1), the parametric equations of the given curve are as follows, x = 2 + 1 2 cos t + 1 3 sin t (3) y = 2 − 1 2 cos t + 1 3 sin t (4) z = 1 + 1 3 sin t (5) Simplifying equation (3) as follows, ( x − 2 ) 2 = ( 1 2 cos t + 1 3 sin t ) 2 ( x − 2 ) 2 = 1 2 cos 2 t + 1 3 sin 2 t + 2 6 cos t sin t (6) Simplifying equation (4) as follows, ( y − 2 ) 2 = ( − 1 2 cos t + 1 3 sin t ) 2 ( y − 2 ) 2 = 1 2 cos 2 t + 1 3 sin 2 t − 2 6 cos t sin t (7) Simplifying equation (5) as follows, ( z − 1 ) 2 = 1 3 sin 2 t (8) Adding equation (6), (7), and (8) as follows, ( x − 2 ) 2 + ( y − 2 ) 2

Thomas' Calculus: Early Transcendentals plus MyLab Math with Pearson eText -- Title-Specific Access Card Package (14th Edition)

14th Edition

ISBN: 9780134768496

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 13.1, Problem 38E

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Prove that the vector valued function r(t) moving in the circle of the radius 1 centered at the point (2,2,1) and lying in the plane x+y−2z=2.

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Chapter 13.1, Problem 37E

Chapter 13.1, Problem 39E

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Chapter 13 Solutions

Thomas' Calculus: Early Transcendentals plus MyLab Math with Pearson eText -- Title-Specific Access Card Package (14th Edition)

Ch. 13.1 - In Exercises 1–4, find the given limits. 1. Ch. 13.1 - In Exercises 1–4, find the given limits. 2. Ch. 13.1 - In Exercises 1–4, find the given limits. 3. Ch. 13.1 - In Exercises 1–4, find the given limits. 4. Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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Prove that the vector valued function r ( t ) moving in the circle of the radius 1 centered at the point ( 2 , 2 , 1 ) and lying in the plane x + y − 2 z = 2 .

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Prove that the vector valued function r(t) moving in the circle of the radius 1 centered at the point (2,2,1) and lying in the plane x+y−2z=2.

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Chapter 13 Solutions