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Math Help - Position vector...

  1. #1
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    Position vector...

    My lecturer occasionally writes his position vectors as a matrix, as follows:

     \vec{r} = \left( \begin{array}{ccc}<br />
0 & -r_z & r_y  \\<br />
r_z & 0 & -r_x \\<br />
-r_y & r_x & 0 \end{array} \right)

    Where does this come from? Why does he use it? Is it equivalent to  \vec{r} = \left( \begin{array}{ccc}<br />
r_x   \\<br />
r_y \\<br />
r_z \end{array} \right)

    For example, he uses it in deriving Newton's 2nd Law for Rotational Motion, as I have attached as a JPEG.
    Attached Thumbnails Attached Thumbnails Position vector...-moment-inertia.jpg  
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  2. #2
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    Quote Originally Posted by Mush View Post
    My lecturer occasionally writes his position vectors as a matrix, as follows:

     \vec{r} = \left( \begin{array}{ccc}<br />
0 & -r_z & r_y \\<br />
r_z & 0 & -r_x \\<br />
-r_y & r_x & 0 \end{array} \right)

    Where does this come from? Why does he use it? Is it equivalent to  \vec{r} = \left( \begin{array}{ccc}<br />
r_x \\<br />
r_y \\<br />
r_z \end{array} \right)

    For example, he uses it in deriving Newton's 2nd Law for Rotational Motion, as I have attached as a JPEG.
    Your lecturer is giving a matrix representation of the vector resulting from a cross product.
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  3. #3
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    Quote Originally Posted by The Second Solution View Post
    Your lecturer is giving a matrix representation of the vector resulting from a cross product.
    How does one derive this?
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