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    Could someone explain how the left is equal to the right hand side.

     \int_C \textbf{c}\phi \cdot \text{d\textbf{r}} = \textbf{c} \cdot \int_C \phi \hspace{0.08cm} \text{d\textbf{r}} , where  \textbf{c} is a constant vector

    I know the dot product identities, but i don't know how to apply them here since we have integrals involved!
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    Phi is a scalar function of vector r, right?
    It all drops out if you use suffix notation. I can LaTeX it up for you if you like, but it might take me a while (I just started the attempt and it seems to be a perversely complicated expression to put into LaTeX.)
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    I hope this picture is big enough… I gave up on the LaTeX and wrote it in Mathematica, but it's not valid syntax so it doesn't want to output it as TeX.
    Name:  Screen Shot 2013-04-10 at 21.22.56.png
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Size:  8.5 KB
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    (Original post by Smaug123)
    Phi is a scalar function of vector r, right?
    It all drops out if you use suffix notation. I can LaTeX it up for you if you like, but it might take me a while (I just started the attempt and it seems to be a perversely complicated expression to put into LaTeX.)
    Yes phi is a scalar function ϕ(x,y,z). I can't seem to understand what you have shown above. I still don't get it..
    Why are they equal or how to you get from the left to the right hand side?
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    Just write it in components (this is essentially what the suffix notation is).

    e.g. put \mathbf{c}:=(c_1,c_2,c_3) &cetera
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    (Original post by amy1e3)
    Yes phi is a scalar function ϕ(x,y,z). I can't seem to understand what you have shown above. I still don't get it..
    I've never heard of suffix notation which makes it harder to understand. Where is the dot products in your image gone?
    Ah, if you've not done suffix notation then my explanation will be really hard to understand :P it's a very convenient notation for vectory stuff, but it takes some getting used to, so I'll write it out "longhand", using the notation "x with subscript i means the ith component of x" - so (5,2,3)_1 = 5, and if c=(5,2,3) then c_1 = 5.
    Name:  Screen Shot 2013-04-10 at 22.54.40.png
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    Hopefully that's more comprehensible - I'll have another look tomorrow morning if you still don't see it (I know it could be a bit of a conceptual jump if you've not really covered the idea of evaluating vectors componentwise before!)
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    (Original post by Mark85)
    Just write it in components (this is essentially what the suffix notation is).

    e.g. put \mathbf{c}:=(c_1,c_2,c_3) &cetera
    I see what the notation is but how does this help?
    I don't seem to know what to do.
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    (Original post by amy1e3)
    I see what the notation is but how does this help?
    Because if you know that (where c and x are vectors) c = x, then you know that c_1 = x_1, and so on, so you can turn vector equations into a system of scalar equations. You use the suffices to tell you "where in the system of equations you are" - which equation you're referring to.
    The key thing is that c.x = c1x1+c2x2+c3x3.
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    (Original post by amy1e3)
    I see what the notation is but how does this help?
    I don't seem to know what to do.
    Because (presumably) you know how to expand a dot product written in components. If not then google it or look in your book/notes.

    The other poster did this to explain your integral but used slightly less familiar notation. To be fair, it shouldn't take to long to just translate what he wrote into the normal component notation that you are used to if you read his posts.

    In any case, you can just go ahead and write out the whole integral in components (i.e. write every term in components) and then recall or look up how to expand a dot product of two vectors written in components and apply that to the integral.
 
 
 
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