Chapter 13.3, Problem 56E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Show that the osculating plane at every point on the curve

To determine

**To show**: The osculating plane at every point on the curve

Explanation

**Given data:**

Curve is

**Formula used:**

Write the expression for tangent vector of a vector function

Here,

Write the equation of osculating plane with vector

Write the expression for binormal vector of vector function

Consider the two three-dimensional vector functions such as

**Cross product of vectors:**

Write the expression for cross product of vectors

Write the expression for magnitude of vector

Here,

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

Find the value of

Find the value of

Substitute

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

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