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Lines and planes

  1. Nov 18, 2008 #1
    1. The problem statement, all variables and given/known data

    show that the plane 2x - y + 4z = 81

    never intersects the line


    2. Relevant equations


    3. The attempt at a solution

    I wanted to show that the line and the plane were parallel. So the unit vector for the line would be 3i + 3j + 1k
    Then I get confused how to show this is parallel to the plane
    Planes don't have unit vectors do they ?
    The vector normal to the plane i suppose is 2i + -j + 4z

    So if the two were parallel a dot b would be = 0
    but this doesnt work ... help
  2. jcsd
  3. Nov 18, 2008 #2


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    I think the unit vector of the line is 3i+2j+k. But that doesn't change anything, the direction vector and the normal vector still aren't perpendicular. That can only mean that the line and the plane must intersect. There is probably a typo in the problem.
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