   Chapter 12.5, Problem 33E

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# Finding Curvature In Exercises 23-28, find the curvature of the plane curve at the given value of the parameter. r ( t ) = t i + t 2 j = t 2 2 k

To determine

To calculate: The curvature of the curve whose position vector is r(t)= t i+ t2 j + t22k.

Explanation

Given:

The position vector of the curve is r(t)= t i+ t2 j + t22k.

Formula Used:

The curvature of the curve r(t)= t i+ t2 j + t22k at t is K=r(t)×r(t)r(t)3.

Calculation:

Consider the position vector of the curve,

r(t)= t i+ t2 j + t22k

Differentiate r(t) with respect to t

r(t)=i+2t j+t k

Find the absolute value of r(t),

r(t)=1+4t2+t2

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

r(t)=2j+k

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