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Math Help - Planes and lines in Wolfram Mathematica

  1. #1
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    Planes and lines in Wolfram Mathematica

    I am trying to check if the points A(1,1,1) B(2,3,1) are on the plane.

    Code:
    2x + 3y - z == 6 (x -> 2, y -> 3,  z -> 1)
    It should return false or true. What am I doing wrong?
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  2. #2
    A Plied Mathematician
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    Try this:

    Code:
    2x + 3y - z == 6 /. {x -> 2, y -> 3, z -> 1}.
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  3. #3
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    Thank you, it works.
    But how can I get the vertex of a plane with the equation -2z + 4 = 0, and the line (4+t,1+5t,1+3t)?
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  4. #4
    A Plied Mathematician
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    Try this code:

    Code:
    Solve[(-2z + 4 == 0) /. {x -> 4 + t, y -> 1 + 5t, z -> 1 + 3t}, t].
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