To prove: There is a number τ (torsion) such that d B d s = − τ N using the following steps: (a) Show that d B d s = T × d N d s and also, conclude that d B d s is orthogonal to T. (b) Show that d B d s is orthogonal to B and also, differentiate B ⋅ B = 1 with respect to s. (c) Conclude that d B d s is a multiple of N.

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Answer 1

Question

Chapter 14.4, Problem 86E

To determine

To prove:

There is a number $τ$ (torsion) such that $\frac{d B}{d s} = - τ N$ using the following steps:

(a) Show that $\frac{d B}{d s} = T \times \frac{d N}{d s}$ and also, conclude that $\frac{d B}{d s}$ is orthogonal to T.

(b) Show that $\frac{d B}{d s}$ is orthogonal to B and also, differentiate $B \cdot B = 1$ with respect to s.

(c) Conclude that $\frac{d B}{d s}$ is a multiple of N.

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Answer 2

Question

Chapter 14.4, Problem 86E

To determine

To prove:

There is a number $τ$ (torsion) such that $\frac{d B}{d s} = - τ N$ using the following steps:

(a) Show that $\frac{d B}{d s} = T \times \frac{d N}{d s}$ and also, conclude that $\frac{d B}{d s}$ is orthogonal to T.

(b) Show that $\frac{d B}{d s}$ is orthogonal to B and also, differentiate $B \cdot B = 1$ with respect to s.

(c) Conclude that $\frac{d B}{d s}$ is a multiple of N.

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Answer 3

Question

Chapter 14.4, Problem 86E

To determine

To prove:

There is a number $τ$ (torsion) such that $\frac{d B}{d s} = - τ N$ using the following steps:

(a) Show that $\frac{d B}{d s} = T \times \frac{d N}{d s}$ and also, conclude that $\frac{d B}{d s}$ is orthogonal to T.

(b) Show that $\frac{d B}{d s}$ is orthogonal to B and also, differentiate $B \cdot B = 1$ with respect to s.

(c) Conclude that $\frac{d B}{d s}$ is a multiple of N.

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Answer 4

Question

Chapter 14.4, Problem 86E

To determine

To prove:

There is a number $τ$ (torsion) such that $\frac{d B}{d s} = - τ N$ using the following steps:

(a) Show that $\frac{d B}{d s} = T \times \frac{d N}{d s}$ and also, conclude that $\frac{d B}{d s}$ is orthogonal to T.

(b) Show that $\frac{d B}{d s}$ is orthogonal to B and also, differentiate $B \cdot B = 1$ with respect to s.

(c) Conclude that $\frac{d B}{d s}$ is a multiple of N.

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Answer 5

Chapter 14.4, Problem 86E

To determine

To prove:

There is a number $τ$ (torsion) such that $\frac{d B}{d s} = - τ N$ using the following steps:

(a) Show that $\frac{d B}{d s} = T \times \frac{d N}{d s}$ and also, conclude that $\frac{d B}{d s}$ is orthogonal to T.

(b) Show that $\frac{d B}{d s}$ is orthogonal to B and also, differentiate $B \cdot B = 1$ with respect to s.

(c) Conclude that $\frac{d B}{d s}$ is a multiple of N.

Answer 6

Chapter 14.4, Problem 86E

To determine

To prove:

There is a number $τ$ (torsion) such that $\frac{d B}{d s} = - τ N$ using the following steps:

(a) Show that $\frac{d B}{d s} = T \times \frac{d N}{d s}$ and also, conclude that $\frac{d B}{d s}$ is orthogonal to T.

(b) Show that $\frac{d B}{d s}$ is orthogonal to B and also, differentiate $B \cdot B = 1$ with respect to s.

(c) Conclude that $\frac{d B}{d s}$ is a multiple of N.

Answer 7

Chapter 14.4, Problem 86E

To determine

To prove:

There is a number $τ$ (torsion) such that $\frac{d B}{d s} = - τ N$ using the following steps:

(a) Show that $\frac{d B}{d s} = T \times \frac{d N}{d s}$ and also, conclude that $\frac{d B}{d s}$ is orthogonal to T.

(b) Show that $\frac{d B}{d s}$ is orthogonal to B and also, differentiate $B \cdot B = 1$ with respect to s.

(c) Conclude that $\frac{d B}{d s}$ is a multiple of N.

Answer 8

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Answer 9

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Answer 10

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Answer 11

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

Solution Summary: The author proves that there is a number (torsion) such that D B d s is orthogonal to T.

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Chapter 14 Solutions

Solution Summary: The author proves that there is a number (torsion) such that D B d s is orthogonal to T.

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To prove: There is a number τ(torsion) such that dBds=−τN using the following steps: (a) Show that dBds=T×dNds and also, conclude that dBds is orthogonal to T. (b) Show that dBds is orthogonal to B and also, differentiate B⋅B=1 with respect to s. (c) Conclude that dBds is a multiple of N.

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Chapter 14 Solutions