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Math Help - find vector same direction as .. but has length ..

  1. #1
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    find vector same direction as .. but has length ..

    Hi having trouble understanding this. Question asks find the vector that has same direction as -2i+4j+2k but that has length 6.

    To get the unit vector is did this.
    <br />
\begin{array}{l}<br />
 \hat u = \frac{v}{{||v||}} \\ <br />
  = \frac{1}{{\sqrt {24} }} <  - 2,4,2 >  \\ <br />
  = \frac{1}{{2\sqrt 6 }} <  - 2,4,2 >  \\ <br />
 \end{array}<br />

    Then to find the vector in that direction but length 6, I thought you just multiplied the unit vector by 6. So I get this
    <br />
\begin{array}{l}<br />
  = \frac{6}{{2\sqrt 6 }} < 2,4,2 >  \\ <br />
  = 3\sqrt 6  < 2,4,2 >  \\ <br />
 \end{array}<br />

    But the answer is
    <br />
\sqrt 6  <  - 1,2,1 > <br />
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  2. #2
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    \frac{1}{2\sqrt{6}} \langle -2,4,2 \rangle  =   \frac{1}{\sqrt{6}} \langle -1,2,1 \rangle

    multiply by 6 ...

    \frac{6}{\sqrt{6}} \langle -1,2,1 \rangle = \sqrt{6} \langle -1,2,1 \rangle
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  3. #3
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    Thanks. Was pretty simple algebra. Whoops.
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