Chapter 13, Problem 7RCC

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

(a) Write formulas for the unit normal and binormal vectors of a smooth space curve **r**(*t*).

(b) What is the normal plane of a curve at a point? What is the osculating plane? What is the osculating circle?

**(a)**

To determine

**To Write:** The formula for the unit normal vector of a smooth space curve

Explanation

A point *P* on a smooth space curve

As

At any point where,

Thus, the formula for the unit normal vector of a smooth space curve

**To Write:** The formula for the binormal vector of a smooth space curve

**(b)**

To determine

**To explain:** The normal plane of a curve at a given point, osculating plane and osculating circle.

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