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Math Help - How to find unit vector

  1. #1
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    How to find unit vector

    Say for example v = <3,4>

    I was taught to divide each component by the magnitude in order to get the unit vector, i.e.

    3^2 + 4^2 = ||v||^2
    5 = ||v||

    So the unit vector of that vector is <3/5,4/5> or 1/5<3,4>

    But if I forgot that I had to divide the components by the magnitude, I would not know how to get the unit vector. So I guess I am asking why you divide the components by the magnitude in order to get the unit vector?
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  2. #2
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    Re: How to find unit vector

    Quote Originally Posted by daigo View Post
    But if I forgot that I had to divide the components by the magnitude, I would not know how to get the unit vector. So I guess I am asking why you divide the components by the magnitude in order to get the unit vector?
    Unit vector means a vector of length 1. That is why.
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  3. #3
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    Re: How to find unit vector

    If the vector is <a, b> then its length is, as you say, \sqrt{a^2+ b^2. If you multiply the entire vector, and so each component, by that, you have
    \left<\frac{a}{\sqrt{a^2+b^2}}, \frac{b}{\sqrt{a^2+ b^2}}\right> and its length is
    \sqrt{\left(\frac{a}{\sqrt{a^2+ b^2}}\right)^2+ \left(\frac{b}{\sqrt{a^2+ b^2}}\right)^2}= \sqrt{\frac{a^2}{a^2+ b^2}+ \frac{b^2}{a^2+ b^2}}
    = \sqrt{\frac{a^2+ b^2}{a^2+ b^2}}= 1
    Thanks from daigo
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