Chapter 13.3, Problem 48E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find the vectors **T, N,** and **B** at the given point.

**48. r**(*t*) = ⟨cos *t*, sin *t*, ln cos *t*⟩, (1, 0, 0)

To determine

**To find**: The vectors **T**, **N**, and **B** of vector function

Explanation

**Given data:**

Vector function

**Formula used:**

Write the expression for tangent vector of a vector function

Here,

Write the expression for normal vector of vector function

Here,

Write the expression for binormal vector of vector function

Consider the two three-dimensional vector functions such as

**Cross product of vectors:**

Write the expression for cross product of vectors

Write the expression for magnitude of vector

Here,

*x*, *y*, and *z*-coordinates of vector respectively.

Write the vector function.

Equate the components of

Hence, the value of *t* is 0.

Apply differentiation with respect to *t* on both sides of equation (4).

Find the value of

Substitute

Substitute 0 for *t*,

Apply differentiation with respect to *t* on both sides of equation (5)

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