a. Explanation Given: An object moves along a path r ( t ) = 〈 a cos t + b sin t , c cos t + d sin t , e cos t + f sin t 〉 for 0 ≤ t ≤ 2 π . Calculation: Substitute t = 0 in r ( t ) = 〈 a cos t + b sin t , c cos t + d sin t , e cos y + f sin t 〉 as follows, r ( 0 ) = 〈 a cos ( 0 ) + b sin ( 0 ) , c cos ( 0 ) + d sin ( 0 ) , e cos ( 0 ) + f sin ( 0 ) 〉 = 〈 a ( 1 ) + b ( 0 ) , c ( 1 ) + d ( 0 ) , e ( 1 ) + f ( 0 ) 〉 = 〈 a , c , e 〉 Thus, the component of r (0) is 〈 a , c , e 〉 . Consider the vector r ( t ) = 〈 a cos t + b sin t , c cos t + d sin t , e cos y + f sin t 〉 for 0 ≤ t ≤ 2 π . Compute r ( t ) × r ( 0 ) as follows, r ( t ) × r ( 0 ) = 〈 a cos t + b sin t , c cos t + d sin t , e cos t + f sin t 〉 × 〈 a , c , e 〉 Use cross multiplication method to obtain r ( t ) × r ( 0 ) , r ( t ) × r ( 0 ) = ( i j k a cos t + b sin t c cos t + d sin t b. To determine To find: The conditions on a , b , c , d, e, and f when its satisfies that the curve described by r is a circle.

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 11.7, Problem 83E

To determine

To show: The curve describes by r lies in a plane.

To determine

To find: The conditions on a, b, c, d, e, and f when its satisfies that the curve described by r is a circle.

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Chapter 11.7, Problem 82E

Chapter 11.8, Problem 1E

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Calculus: Early Transcendentals (2nd Edition)

Ch. 11.1 - Interpret the following statement: Points have a...Ch. 11.1 - What is a position vector?Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Given a position vector v, why are there...Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - If u = u1, u2 and v = v1, v2, how do you find u +...Ch. 11.1 - Prob. 10E

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The curve describes by r lies in a plane.

Solution Summary: The author explains that the curve described by r lies in a plane.