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## Homework Statement

F = 3x-y+2z in newtons

the line that it follows is -x+y+2z

What is the work done

## Homework Equations

W=f*d

## The Attempt at a Solution

I am guessing

3x^2 -y^2+2z^2=w

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- Thread starter ex81
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F = 3x-y+2z in newtons

the line that it follows is -x+y+2z

What is the work done

W=f*d

I am guessing

3x^2 -y^2+2z^2=w

- #2

cepheid

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If they do, then your answer is not quite right. What is the definition of the dot product in Cartesian coordinates?

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As to the dot product, I have no clue. It would have been nice if it was ever covered....

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cepheid

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As to the dot product, I have no clue. It would have been nice if it was ever covered....

One way to evaluate the dot product of two vectors

where i, j, and k are

Now, just using the ordinary distributive property of multiplication to expand out this product of two trinomials, you'd get

Now, another consequence of the definition of a dot product is that the dot product of a vector with itself is just equal to the magnitude of that vector, squared. Hence,

- #5

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I had part of a class way back in Trig that vaguely talked about vector multiplication but since it was the day before the final it was considered a "bonus" lesson. Yeah, my physics professor, and the word teach don't exactly mix.

Or do the alpha characters just go away, and thus I would have zero as the answer

- #6

cepheid

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I had part of a class way back in Trig that vaguely talked about vector multiplication but since it was the day before the final it was considered a "bonus" lesson. Yeah, my physics professor, and the word teach don't exactly mix.

Or do the alpha characters just go away, and thus I would have zero as the answer

Well, unless if x, y and z are unit vectors (i.e. they correspond to what I called i, j, and k), your vectors don't really make sense.

Alternatively, rather than being constant, maybe the vectors are functions of position (x,y,z) in 3D space so that F(x,y,z) = 3x - y + 2z. But this is less likely, because if it is what is meant, then you're still missing one or more unit vectors to tell you what the direction of F is. This would also mean you wouldn't be able to solve the problem with a simple dot product. In any case,

- #7

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Force = 3x-y+2z (technically the way it was stated is "component 3 is in newtons")

Line = -x +y+2z (also stated as "- is in meters")

Find the work, ergo W=F*d

I am assuming that when my professor put line, he meant straight, and that was the distance.

Therefore it should look something like

Force * line = work

(3*-1)+(-1+1)+(2*2)

(-3)+(-1)+(4)

which equals zero

P.S. all of the x, y, and z had the "carat" on top of them.

- #8

cepheid

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If, and I do stress the IF I am understanding your explanation of the dot product then it would follow like this:

Force = 3x-y+2z (technically the way it was stated is "component 3 is in newtons")

Line = -x +y+2z (also stated as "- is in meters")

Find the work, ergo W=F*d

I am assuming that when my professor put line, he meant straight, and that was the distance.

Therefore it should look something like

Force * line = work

(3*-1)+(-1+1)+(2*2)

(-3)+(-1)+(4)

which equals zero

That's exactly right. Take another look at the very last equation in my previous post, and you'll see that it says the following. To compute the dot product of the two vectors:

1. multiply their x-components together

2. multiply their y-components together

3. multiply their z-components together

4. Take the sum of these three products.

So, you have done it correctly! Since the dot product is zero, the force and displacement vectors must be perpendicular to each other.

P.S. all of the x, y, and z had the "carat" on top of them.

Okay, then this all makes perfect sense. Those are UNIT VECTORS. In a Cartesian coordinate system, any vector can be resolved into three components. If you look carefully at the expression, you'll see that what it is saying is that the vector is the sum of three individual vectors, one of which points entirely in the x-direction, one of which points entirely in the y-direction, and one of which points entirely in the z-direction. Each "unit vector" has the corresponding component as its coefficient. In other words, the unit vectors (which have length 1) have each been "scaled" to the right length for that component of the vector. That's what the notation means.

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Yay!! Thanks for the explanation :D

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