Problem

For the following exercises, find the work done. …

01:31

Problem 49 Easy Difficulty

For the following exercises, find the work done.
Find the work done by vector field $\mathbf{F}(x, y, z)=x \mathbf{i}+3 x y \mathbf{j}-(x+z) \mathbf{k}$ on a particle moving along a line segment that goes from $(1,4,2)$ to $(0,5,1) .$

Answer

8 work unit

Topics

Vectors

Vector Calculus

Introduction to Vectors

Book Cover for Calculus Volume 3

Calculus Volume 3

Chapter 6

Vector Calculus

Section 2

Line Integrals

Discussion

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Video Transcript

Okay, so we're giving the, uh the field f we're just equals two x three x y naked Max. Want to see? We're looking for the work Done from 0 to 1. So bye. The fury of the work theory We have, um f comes the are over dt. So the derogative of replacements The displacements operator thes placements times the operator dt Ah, Plug it in. We have 0 to 1. So the first, um, components will be one minus t. And 2nd 1 will be netting three times t squared among the three t plus four and to t minus three in the Vetter for the directive of the our of our will be making 11 That one. And did he? And this is a who's in the product before into better. So plug everything in. We have necking 30 square, minus 20 plus 14 dc And the answer is eight

YZ

Yiming Z.

University of Illinois at Urbana-Champaign

Topics

Vectors

Vector Calculus

Introduction to Vectors

Book Cover for Calculus Volume 3

Calculus Volume 3

Chapter 6

Vector Calculus

Section 2

Line Integrals

Top Precalculus Educators

Lily A.

Johns Hopkins University

GH

Grace H.

Numerade Educator

MC

Megan C.

Piedmont College

Joseph L.

Boston College