Explanation Given info. r → ( t ) = ( sin t , − cos t , sin t ) Concept used: B → ( t ) = r ' ( t ) × r " ( t ) ‖ r ' ( t ) × r " ( t ) ‖ Calculation: r → ( t ) = ( sin t , − cos t , sin t ) r → ' ( t ) = ( cos t , sin t , cos t ) r → " ( t ) = ( − sin t , cos t , − sin t ) ( use d d t ( sin t ) = cos t , d d t ( cos t ) = − sin t ) ( r ' ( t ) × r " ( t ) ) = ( cos t , sin t , cos t ) × ( − sin t , cos t , − sin t ) ( vector product in determinant form ) = | i ∧ j ∧ k ∧ cos t sin t cos t − sin t cos t − sin t | Expanding 3 rd order determinant into second order = i ∧ | sin t cos t cos t − sin t | − j ∧ | cos t cos t − sin t − sin t | + k ∧ | cos t sin t − sin t cos t | Expanding 2 nd order determinant = i ∧ ( − sin 2 t − cos 2 t ) − j ∧ ( − cos t ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.4, Problem 92E

To determine

Use the formula from the preceding problem to find $\vec{B}$ for the space curve given by

$\vec{r} (t) = (\sin t, - \cos t, \sin t)$ Conclude that the space lies in a plane.

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Chapter 14.4, Problem 91E

Chapter 14.4, Problem 93E

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Chapter 14 Solutions

CALCULUS (CLOTH)

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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Use the formula from the preceding problem to find B → for the space curve given by r → ( t ) = ( sin t , − cos t , sin t ) Conclude that the space lies in a plane.

Solution Summary: The author concludes that the space lies in a plane by using the formula from the preceding problem.

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Use the formula from the preceding problem to find $\vec{B}$ for the space curve given by

$\vec{r} (t) = (\sin t, - \cos t, \sin t)$ Conclude that the space lies in a plane.

Want to see the full answer?

Chapter 14 Solutions

Use the formula from the preceding problem to find B → for the space curve given by r → ( t ) = ( sin t , − cos t , sin t ) Conclude that the space lies in a plane.

Solution Summary: The author concludes that the space lies in a plane by using the formula from the preceding problem.

Videos

Use the formula from the preceding problem to find B→ for the space curve given by r→(t)=(sint,−cost,sint) Conclude that the space lies in a plane.

Want to see the full answer?

Chapter 14 Solutions

Use the formula from the preceding problem to find $\vec{B}$ for the space curve given by

$\vec{r} (t) = (\sin t, - \cos t, \sin t)$ Conclude that the space lies in a plane.