Chapter 13.3, Problem 21E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Use Theorem 10 to find the curvature.

**21. r**(*t*) = *t*^{3} **j** + *t*^{2} **k**

To determine

**To find**: The curvature of

Explanation

**Given data:**

The vector function

**Formula used:**

Consider the three three-dimensional vectors such as

**Cross product of vectors:**

Write the expression for cross product of vectors **a** and **b**

Write the expression for curvature of vector function **r** according to theorem 10.

Here,

Write the expression for magnitude of vector

Here,

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

Write the vector equation.

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

Find the value of

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

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