Chapter 13, Problem 11RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

For the curve given by **r**(t) = ⟨sin^{3} *t*, cos^{3} *t*, sin^{2} *t*⟩, 0 ≤ *t* ≤ π/2, find

(a) the unit tangent vector,

(b) the unit normal vector,

(c) the unit binomial vector, and

(d) the curvature.

**(a)**

To determine

**To find:** The unit tangent vector

Explanation

**Formula used:**

Write the expression to find the unit tangent vector

Here,

Write the required differential formulae to find the tangent vector

**Calculation of tangent vector**
**:**

To find the derivative of the vector function, differentiate each component of the vector function.

Differentiate each component of the vector function

Rewrite and compute the expression as follows.

**Calculation of unit tangent vector**
**:**

Substitute

**(b)**

To determine

**To find:** The unit normal vector

**(c)**

To determine

**To find:** The unit binormal vector

**(d)**

To determine

**To find:** The curvature

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