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Math Help - Plane Parallel to line

  1. #1
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    Plane Parallel to line

    Determine the value of c such that the plane with equation 2x+3y-cz-8=0 is parallel to the line with equation x=1+2t, y=2+3t, z=-1+t

    How would I go about doing this question?
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  2. #2
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    Re: Plane Parallel to line

    Quote Originally Posted by IanCarney View Post
    Determine the value of c such that the plane with equation 2x+3y-cz-8=0 is parallel to the line with equation x=1+2t, y=2+3t, z=-1+t
    A line is parallel to a plane if and only if its direction vector is perpendicular to the normal of the plane.
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    Re: Plane Parallel to line

    Quote Originally Posted by Plato View Post
    A line is parallel to a plane if and only if its direction vector is perpendicular to the normal of the plane.
    Direction vector: (2,3,1) and the normal of the plane is (2,3, c), right? What would I do now? Cross product? But how would I find the c value?
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    Re: Plane Parallel to line

    Quote Originally Posted by IanCarney View Post
    Direction vector: (2,3,1) and the normal of the plane is (2,3, c), right? What would I do now? Cross product? But how would I find the c value?
    Cross products are not in play here.
    Two vectors are perpendicular it their dot product is zero.
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