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Quick vectors question

  1. Sep 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a unit vector that has the same direction as the given vector.

    8i - j + 4k

    3. The attempt at a solution

    I got

    sqrt(81) * (8i - j + 4k). The book has 1/9 * (8i-j+4k).

    Why exactly is that?


    ------------
    Another question :

    Find a vector that has the same direction as -2i+4j+2z but has length 6.

    I think I could find the unit vector by dividing each component by its magnitude, and
    then multiply it by a scaler number, 6.

    Can you comment on that?
     
  2. jcsd
  3. Sep 10, 2009 #2

    rock.freak667

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    any vector parallel or in the same direction as 8i - j + 4k has a vector form of λ(8i - j + 4k) where λ=scalar.


    So all vectors parallel to 8i - j + 4k can be written as 8λi-λj+4λk


    Unit vector means magnitude=1

    so |8λi-λj+4λk|=1

    you can find λ from the definition of the magnitude of a vector.

    For the next question, you can find it like that as well.
     
  4. Sep 10, 2009 #3

    LCKurtz

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    Science Advisor
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    Gold Member

     
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