Chapter 13.3, Problem 66E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find the curvature and torsion of the curve *x* = sinh *t*. *y* = cosh *t*, *z* = *t* at the point (0, 1, 0).

To determine

**To find**: The curvature and torsion of the curve

Explanation

**Given data:**

Parametric equation of curve are

**Formula used:**

Write the expression for curvature of curve

Here,

Write the expression for torsion of curve

Consider the two three-dimensional vector functions such as

**Cross product of vectors:**

Write the expression for cross product of vectors

**Dot product of vectors:**

Write the expression for dot product of vectors

Write the expression for curve

Substitute
*x*,
*y*, and *t* for *z*,

Equate the components of

Hence, *t* value is 0.

Find the value of

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

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

Find the value of

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