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Finding values to make a unit vector

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Find all values of a such that w=ai+[itex]\frac{a}{8}[/itex]j is a unit vector.

    2. Relevant equations
    unit vector has length of 1. and for a vector v unit vectors would be v/magv

    3. The attempt at a solution
    1=magw=\sqrt (a2+(a/8)2)
    1=a2+(a2/64)
    64=2a2
    32=a2
    a=[itex]\sqrt{32}[/itex]

    i know that the solution is: +/- [itex]\frac{8}{\sqrt{65}}[/itex] but am at a loss as to how it was obtained. any help is appreciated.
     
  2. jcsd
  3. Sep 17, 2012 #2
    sqrt(a^2+a^2/64)=1
    so this means sqrt((64a^2+a^2)/64)=1
    so sqrt(65a^2/64)=1
    this means 65a^2/64=1
    and then you get the result
     
  4. Sep 17, 2012 #3

    Mark44

    Staff: Mentor

    Your mistake is above. Multiply each term on the right side by 64. You don't get 2a2.
     
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