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Math Help - Unghle

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    21

    Unghle

    Determine the unghle betwwen:
    P1:x+y-z-1=0
    P2:x+2y-7=0
    when P=Plan
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    One normal vector \overrightarrow{n_1} to P1 has coordinates (1,1,-1) which are the coefficients of x, y and z in P1 equation

    One normal vector \overrightarrow{n_2} to P2 has coordinates (1,2,0)

    The angle \theta between P1 and P2 is the same as the one between \overrightarrow{n_1} and \overrightarrow{n_1}

    The dot product is
    \overrightarrow{n_1} \cdot \overrightarrow{n_2}=||\overrightarrow{n_1}|| \cdot ||\overrightarrow{n_1}|| \cdot \cos \theta

    Which gives
    3 = \sqrt{3} \: \sqrt{5} \: \cos \theta

    \cos \theta = \frac{\sqrt{3}}{\sqrt{5}}
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