Chapter 13.3, Problem 58E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

The *rectifying plane* of a curve at a point is the plane that contains the vectors **T** and **B** at that point. Find the rectifying plane of the curve **r**(*t*) = sin *t* **i** + cos *t* **j** + tan *t* **k** at the point

To determine

**To find**: The rectifying plane of curve

Explanation

**Given data:**

The curve is

**Formula used:**

Write the expression for tangent vector of a vector function

Here,

Write the equation of plane with vector

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.

The rectifying plane contains vectors

Equate the components of

Hence, the value of *t* is

Find the value of

Find the value of

Substitute

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

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