Chapter 12.5, Problem 34E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
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# Finding Curvature In Exercises 29-36, find the curvature of the curve. r ( t ) = 2 t 2 i + t j + 1 2 t 2 k

To determine

To calculate: The curvature of the curve having a position vector r(t)=2t2i+t j+12t2k.

Explanation

Given:

The curve is r(t)=2t2i+t j+12t2k.

Formula Used:

The curvature of the curve at t is K=r(t)×r(t)r(t)3.

Calculation:

Consider the curve,

r(t)=2t2i+t j+12t2k

Differentiate r(t) with respect to t

r(t)=4t i+j+t k

Find the absolute value of r(t),

r(t)=16t2+1+t2

The differentiation of r(t) with respect to t is,

r(t)=4 i+k

The cross product r(t)×r(<

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