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Math Help - Finding a unit vector

  1. #1
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    Finding a unit vector

    Among all the unit vectors in ,
    find the one for which the sum is minimal.
    Hint: , where .
    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by Shapeshift View Post
    Among all the unit vectors \vec{u} = \begin{bmatrix}x\\y\\z\end{bmatrix} in ,
    find the one for which the sum is minimal.
    Hint: , where \vec{v} = \begin{bmatrix}1\\5\\4\end{bmatrix}.
    The dot product \vec{u}\cdot\vec{v} will be minimal when \vec{u} is pointing in the opposite direction to \vec{v}. That suggests taking \vec{u} = \begin{bmatrix}-1\\-5\\-4\end{bmatrix}. But that is not a unit vector. So you will need to divide that vector by its length.

    Is that enough of a hint?
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