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Math Help - Line orthogonal to a plane.

  1. #1
    Junior Member
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    Line orthogonal to a plane.

    The question reads

    "For what values of a and b is the line L othogonal to the plane 8x+4y+8z=14"

    Line L is given in parametric equations.
    x=15+2t
    y=8+at
    z=4+bt

    If someone could give me pointers on how to start this problem is would be great!

    So far, I know:
    Direction vector for the plane is <8,4,8>
    Direction vector for the line is <2,a,b>

    So is the direction vector for the line <2,1,2>?
    Since <8,4,8> would be 4<2,a,b>.
    Correct?

    Or is this a line parallel to the plane? Sorry if this is a dumb question.
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  2. #2
    MHF Contributor

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    Re: Line orthogonal to a plane.

    Your problem is thinking of <8, 4, 8> as the "direction vector" for the plane. A line has a direction vector that points in the direction of the line. A plane has a normal vector. <8, 4, 8> points perpendicular to the plane.
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  3. #3
    Junior Member
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    Re: Line orthogonal to a plane.

    Oh yes. That's correct. Thanks! Going insane over here.
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