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Math Help - Vectors: i + i = ?

  1. #1
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    Vectors: i + i = ?

    Good day folks,

    Just doing some reading about cartesian dot product etc.

    I realise i x j = k, i x i = 0 etc.

    Can someone tell me if there are relations for i + i and i/i ?


    I apologise - I am a bit rusty with this stuff...


    Kind regards.
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  2. #2
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    Re: Cartesian co-ordinates i + i = ?

    Quote Originally Posted by paulbk108 View Post
    Good day folks,

    Just doing some reading about cartesian dot product etc.

    I realise i x j = k, i x i = 0 etc.

    Can someone tell me if there are relations for i + i and i/i ?


    I apologise - I am a bit rusty with this stuff...


    Kind regards.
    i + i = 2i.

    Dividing vectors is not defined so i/i is not defined.

    There are many websites that explain the algebra of vectors in detail, I suggest you use Google to find one.
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  3. #3
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    Re: Cartesian co-ordinates i + i = ?

    Very good. Thank you. Simple.

    What about i + j = ? Or is that not defined as well?


    Regards.
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  4. #4
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    Re: Cartesian co-ordinates i + i = ?

    Th reason I ask:

    I have an example here that goes from

    1.2i + 1.2j + 0.7i + 0.7j
    = 1.2 + 0.7

    I just can't figure out why...

    Regards.
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  5. #5
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    Re: Cartesian co-ordinates i + i = ?

    Quote Originally Posted by paulbk108 View Post
    I have an example here that goes from
    1.2i + 1.2j + 0.7i + 0.7j= 1.2 + 0.7
    That is completely wrong.
    If it is as you posted it then
    1.2i + 1.2j + 0.7i + 0.7j=1.9i+1.9j.

    So please check the exact wording of this problem!
    Please correct any errors.
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  6. #6
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    Re: Cartesian co-ordinates i + i = ?

    I have

    -(Vc)i = -1.2i + 1.2j + 0.7(Vc)i + 0.7(Vc)j

    => -(Vc) = -1.2 + 0.7(Vc)

    Not sure if that makes a difference.
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  7. #7
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    Re: Cartesian co-ordinates i + i = ?

    Quote Originally Posted by paulbk108 View Post
    I have

    -(Vc)i = -1.2i + 1.2j + 0.7(Vc)i + 0.7(Vc)j

    => -(Vc) = -1.2 + 0.7(Vc)

    Not sure if that makes a difference.
    This statement comes from the dark side of the moon. Clear things up ... what is the original problem and what is it asking you to determine?
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  8. #8
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    Re: Cartesian co-ordinates i + i = ?

    Solving for Vca.

    -Vci = (3k) x (0.4i + 0.4j) + ((Vca)cos45i + (Vca)sin45j)
    => -Vci = -1.2i + 1.2j +0.7(Vca)i + 0.7(Vca)j
    => -Vc = -1.2 + 0.7(Vca)
    => 0 = 1.2 + 0.7(Vca)
    => Vca = -1.697 m/s

    => Vc = 2.4 m/s.

    I hope that clears it up. I also hope you can assist me further...


    Regards.
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  9. #9
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    Re: Cartesian co-ordinates i + i = ?

    Quote Originally Posted by paulbk108 View Post
    Solving for Vca.

    -Vci = (3k) x (0.4i + 0.4j) + [(Vca)cos45i + (Vca)sin45j]
    to tell you the honest truth, this makes absolutely no mathematical sense to me.

    is that a cross product at the start?. what does "k" represent?

    why don't you "copy" the original problem, upload it to imageshack, and post it as a link so that someone can make sense of it?
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  10. #10
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    Re: Cartesian co-ordinates i + i = ?

    Attached is the solution in question. Hope now it is a bit clearer.

    Regards.
    Attached Files Attached Files
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  11. #11
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    Re: Cartesian co-ordinates i + i = ?

    Quote Originally Posted by paulbk108 View Post
    I have

    -(Vc)i = -1.2i + 1.2j + 0.7(Vc)i + 0.7(Vc)j

    => -(Vc) = -1.2 + 0.7(Vc)

    Not sure if that makes a difference.
    Writing your equation in LaTeX gives:

    -(V_c)\hat{i} = -1.2\hat{i} + 1.2\hat{j} + 0.7(V_c)\hat{i} + 0.7(V_c)\hat{j}

    Equating the x components, then solving for V_c gives your result.

    Equating the y components gives the same result.
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