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Math Help - Vector equation of a line normal to a plane.

  1. #1
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    Vector equation of a line normal to a plane.

    Can someone please help me find the vector equation for the line through point R(3,0,-3) normal to the plane
    -4x-12y+4z=-24 ?

    I have the normal as n = -4i -12j +4k, but am at lost to the next step.

    Any help will be greatly appreciated.
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  2. #2
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    Re: Vector equation of a line normal to a plane.

    Quote Originally Posted by tammmyl View Post
    Can someone please help me find the vector equation for the line through point R(3,0,-3) normal to the plane
    -4x-12y+4z=-24 ?
    I have the normal as n = -4i -12j +4k, but am at lost to the next step.
    We can use the normal i+3j-k so the the equation of the line is <3,0,-3>+t<1,3,-1>.
    Recall that a line is perpendicular to a plane if it is parallel to the normal of the plane.
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  3. #3
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    Re: Vector equation of a line normal to a plane.

    The obvious point (which I just have to mention) is that when t= 0, this is (3, 0, -3), the given point, and its direction is given by the "slope", <1, 3, -1>, as given by the normal to the plane.
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