# Homework Help - Calculus III / Physics / Force-Work Problem

At the moment, I can't find a similar example in my textbook or in my class notes, and I have looked for one and contemplated this problem for the past hour or so. Can anyone give me an idea of what to do to solve this problem?

A constant force F = -3i -2j -1k acts upon an object moving along a straight line from point (-8,0,-10) to point (-9,9,9). Find the work done if the distance is measured in meters and the magnitude of the force is measured in newtons.

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The work is defined to be $W = \vec{F} \cdot \vec{d}$ (look here: http://en.wikipedia.org/wiki/Work_(physics) )

I assume in your lecture notes the unit vectors $\vec{e}_1 = (1, 0, 0), \vec{e}_2 = (0, 1, 0), \vec{e}_3 = (0, 0, 1)$ are denored $i,j,k$.

Then $\vec{F} = (-3, -2, -1)$ and $\vec{d} = (-9,9,9)-(-8,0,-10)$. Now all you have to do to finish this homework question is to compute the scalar product $\vec{F} \cdot \vec{d}$.

Let me know if you can do this question now or if you need more help.

By the way: if you are satisfied with an answer you should click on the tick to the left of the answer to accept it. If you don't do that, people here will eventually stop answering your questions.

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Thanks for the tip, I didn't know how to accept answers before. –  Math Student Jan 31 '11 at 18:03
@Math Student: That's what I thought ; ) –  Rudy the Reindeer Jan 31 '11 at 21:22

Work is the dot product of the force and the displacement. You have the force as a vector. What is the displacement?

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The displacement seems to be: (-1, 9, 19) –  Math Student Jan 31 '11 at 18:01
@Math Student: right you are –  Ross Millikan Jan 31 '11 at 18:05
Thanks for the help, the work is -34. I got it right. –  Math Student Jan 31 '11 at 18:10