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Math Help - Unit vector

  1. #1
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    Unit vector

    Hey,

    I just want to make sure I correctly understand unit vectors. I know they indicate units of length or magnitude, but how does that play out practically speaking? Take the following example.

    x f(x)=x^2

    1 1
    2 4
    3 9
    4 16

    And so on. In layman's terms, what is exactly going on there? It looks like a simple exponential expression, but is that correct? Probably not, because wouldn't you just write f(x)=x2 (squared)? I just don't quite get the whole concept...

    What if it's f(x)=x^3? How does that play out?

    Thanks in advance!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by SeanC View Post
    Hey,

    I just want to make sure I correctly understand unit vectors. I know they indicate units of length or magnitude, but how does that play out practically speaking? Take the following example.

    x f(x)=x^2

    1 1
    2 4
    3 9
    4 16

    And so on. In layman's terms, what is exactly going on there? It looks like a simple exponential expression, but is that correct? Probably not, because wouldn't you just write f(x)=x2 (squared)? I just don't quite get the whole concept...

    What if it's f(x)=x^3? How does that play out?

    Thanks in advance!
    Ummm... It's a function. For a given x value, you take the cube of it and that's the value of f(x).

    What does this have to do with unit vectors??

    -Dan
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    Quote Originally Posted by topsquark View Post
    Ummm... It's a function. For a given x value, you take the cube of it and that's the value of f(x).

    What does this have to do with unit vectors??

    -Dan
    Haha, now I feel like a genius. A buddy of mine said the "^" symbol is used to indicate a unit vector. Guess not, heh.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by SeanC View Post
    Haha, now I feel like a genius. A buddy of mine said the "^" symbol is used to indicate a unit vector. Guess not, heh.
    hehe, no. "^" indicates powers.

    who is this buddy of yours?
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    hehe, no. "^" indicates powers.

    who is this buddy of yours?
    A math tutor, actually, hahahah. As it was over the phone, maybe he didn't understand what I was describing. I said shift+6...what is that?

    Anyways, thanks for the clarification.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by SeanC View Post
    A math tutor, actually, hahahah. As it was over the phone, maybe he didn't understand what I was describing. I said shift+6...what is that?

    Anyways, thanks for the clarification.
    he may have been refering to a vertical or horizontal shift, did he say shift to the right/left, or just a vertical shift of +6. in that case, he means you take a graph and you shift it up by +6. this happens when you add 6 to a graph.

    see the diagram below for an example. the red graph is x^2 and the blue is x^2 + 6, that is, x^2 shifted up by 6 units.
    Attached Thumbnails Attached Thumbnails Unit vector-shift-quadratic.jpg  
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    Quote Originally Posted by Jhevon View Post
    he may have been refering to a vertical or horizontal shift, did he say shift to the right/left, or just a vertical shift of +6. in that case, he means you take a graph and you shift it up by +6. this happens when you add 6 to a graph.

    see the diagram below for an example. the red graph is x^2 and the blue is x^2 + 6, that is, x^2 shifted up by 6 units.
    Ah, I actually meant the symbol produced by pressing shift+6 (^), which I specified on the call. What you showed, however, does make sense.
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by SeanC View Post
    Ah, I actually meant the symbol produced by pressing shift+6 (^), which I specified on the call. What you showed, however, does make sense.
    haha, oh! ok now i feel like a genius
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    Quote Originally Posted by Jhevon View Post
    haha, oh! ok now i feel like a genius
    My mathematical ignorance wins again. :P
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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by SeanC View Post
    Haha, now I feel like a genius. A buddy of mine said the "^" symbol is used to indicate a unit vector. Guess not, heh.
    For the record, it does, but not as you applied it. However I can think of no way for you to type it without using some kind of text editor.

    For example:
    \hat{i}, \hat{j}, \hat{k}
    are the unit vectors in the x, y, and z directions, respectively.

    -Dan
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  11. #11
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    Quote Originally Posted by topsquark View Post
    For the record, it does, but not as you applied it. However I can think of no way for you to type it without using some kind of text editor.

    For example:
    \hat{i}, \hat{j}, \hat{k}
    are the unit vectors in the x, y, and z directions, respectively.

    -Dan
    Ah yes, I've seen that. Thanks for the clarification.
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