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Math Help - Vectors

  1. #1
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    Vectors

    I need help with the following 2 questions please

    1. Prove that the line x=1+2t, y=-1+3t, z=2+4t is parallel to the plane x-2y+z=6.

    2. Find the distance between the line and the plane in 1.

    thanks
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  2. #2
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    If D is the direction vector of the line and N is the normal vector of the plane then if D \cdot N = 0 then the two are prallel.
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  3. #3
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by smiler View Post
    I need help with the following 2 questions please

    1. Prove that the line x=1+2t, y=-1+3t, z=2+4t is parallel to the plane x-2y+z=6.

    2. Find the distance between the line and the plane in 1.

    thanks
    the line is parallel to the vector v=<2,3,4> and the plane is perpendicular to the vector r=<1,-2,1>

    like what plato said, try to check of the vectors v, r are perpendicular to each other, i.e their dot product is 0, then the line and the plane are parallel..
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