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Math Help - Plane (geometry)

  1. #1
    Member roshanhero's Avatar
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    Plane (geometry)

    The question goes like this-
    Find the equation of the plane containing the lines through the origin with direction cosines proportional to 2,1,-2 and 5,2,-3.
    I have done most of the part,but got confused on this part-
    I got two equations
    5a+2b-3c=0
    2a+b-2c=0
    I just don't know how to apply cross multiplication for a,b and c.
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  2. #2
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    \left| {\begin{array}{rrr}   i & j & k  \\   5 & 2 & { - 3}  \\<br />
   2 & 1 & { - 2}  \\ \end{array} } \right| = i\left| {\begin{array}{rr}<br />
   2 & { - 3}  \\   1 & { - 3}  \\ \end{array} } \right| - j\left| {\begin{array}{rr}   5 & { - 3}  \\   2 & { - 2}  \\ \end{array} } \right| + k\left| {\begin{array}{rr}   5 & 2  \\   2 & 1  \\ \end{array} } \right|
    Now can you finish?
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