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Math Help - Vector problem (solved but I need explanation)

  1. #1
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    Question Vector problem (solved but I need explanation)

    its given

    a(vector) = {2; -3; 6}
    b(vector) = {-1; 2;-2}

    There is an orange line which halfs the angle between two vectors {shown in picture}

    Now problem says:
    Find a vector over orange line {showed in the picture} that length is 2 \sqrt(42)

    note! The problem doesnt say that vectors starts from {0,0,0} point, I just draw the figure to illustrate it more better. The problem doesn't contain any picture with it.

    The answer = {-2,10,8}
    The 2nd answer = {2,-10,-8}

    please explain for me, how to solve it! step by step. Thanks in advance
    Thank you in advance
    Attached Thumbnails Attached Thumbnails Vector problem (solved but I need explanation)-figure.jpg  
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  2. #2
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    I do not really follow the question!
    However, I can give you the expression for the bisector be the two vectors.
    \left\| b \right\|a + \left\| a \right\|b.
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  3. #3
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    The orange line is the bisector of vectors a and b and as plato wrote one vector that directs this line is:


    (if this is not clear say so)

    In our case this leads to a vector c which coordinates are

    c (-1; 5; 4)

    Now any vector colinerar to c "will be" on the orange line, so will have coordinates (-k; 5k; 4k)


    now we want the norm of this vector to be

    this leads to
    k^2+25k^2+16k^2=42 x 4
    k^2=4

    k=2 or k=-2

    And thus the answer.

    Civodul
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