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Math Help - Matrix/projection of vectors problem

  1. #1
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    Post Matrix/projection of vectors problem

    Another problem:

    Use matrix multiplication to find the projection of the vectors (3,4) (2,1) and (-3,2) during rotation for -30 deg. with center in the coordinate start (beginning).

    tnx
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  2. #2
    Member HappyJoe's Avatar
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    I don't see what your problem has to do with projections. Do you just want to find the images of the three vectors under a rotation of -30 degrees?
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  3. #3
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    Yeah sorry bad translation - i meant the images of the three vectors.
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  4. #4
    Member HappyJoe's Avatar
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    It should appear somewhere in your book or in your notes that the matrix that rotates a vector through an angle of v is

    cos(v), -sin(v)
    sin(v), cos(v).

    You can apply this to your specific problem.

    (LaTeX won't work for me at the moment.)
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  5. #5
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    Ok so it will look something like this:
    1.
    cos(-30) -sin(-30)
    sin(-30) cos(-30)

    and the matrix:
    2.
    3 2 -3
    4 1 2
    ?

    what should i do after - should i multiply 1. with 2.?

    EDIT---
    1.
    -sqrt(3) / 2 , 1/2
    -1/2 , -sqrt(3)/2
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  6. #6
    Member HappyJoe's Avatar
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    The matrix in 1. rotates vectors -30 degrees, right. You don't need the matrix in 2. for anything.

    The way the matrix rotates a vector is simply by multiplying the matrix with the vector, so to see where (-3,2) gets rotated, you multiply the matrix in 1. with the column vector

    -3,
    2,

    in that order.
    Last edited by HappyJoe; May 5th 2011 at 10:50 AM. Reason: Spelling.
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  7. #7
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    tnx a lot for your help HappyJoe
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