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Find a tangent & a normal

  1. Sep 21, 2008 #1
    Write a in the form a=a[tex]_{Y}[/tex]T+a[tex]_{N}[/tex]N without finding T and N at the given t-value.

    r=t[tex]\widehat{i}[/tex]+3t[tex]^{2}[/tex][tex]\widehat{j}[/tex]+t[tex]^{2}[/tex]/2[tex]\widehat{k}[/tex] , t=2

    The first thing I did was to find the first derivative. Which turned out to be i+6tj+tk
    Then I found the length [tex]\sqrt{1+37t^{2}}[/tex]
    Then I took the derivative of that to find a[tex]_{T}[/tex] 37t/[tex]\sqrt{37t^{2}+1}[/tex]

    So my question really is, for a[tex]_{N}[/tex] do I really have to plug that mess into [tex]\sqrt{|a|^{2}-a_{T}^{2}}[/tex]
  2. jcsd
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