Chapter 16.2, Problem 41E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the work done by the force field

**F**(*x*, *y*, *z*) *=* `⟨`

*x− y*^{2}, *y − z*^{2}, *z − x*^{2}`⟩`

on a particle that moves along the line segment from (0, 0, 1) to (2, 1, 0).

To determine

**To find:** The work done by the force field

Explanation

**Given data:**

The force field is

The particle moves along the line segment from the point

**Formula used:**

Write the expression to find the work done by the force field

Here,

Write the expression to find the parametric equations for a line segment through the point

Write the expression to find the director vector

**Calculation of direction vector**
** for a line segment:**

Substitute 0 for

**Calculation of parametric equations of line segment:**

Substitute 0 for

Write the vector function from the parametric equations as follows.

Write the force field as follows.

**Calculation of**
**:**

Substitute

**Calculation of**
**:**

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

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