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Homework Help: Parallel plane containing a line

  1. Jan 13, 2010 #1


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    The problem statement, all variables and given/known data
    Find the plane that contains the line x=3+2T, Y=t, Z=8-t and is parallel to the plane 2x + 4y +8z =17.

    The attempt at a solution

    It seemed to me that since the plane is parallel to the plane 2x+4y+8z=17, it must be of the form 2x+4y+8z+D=0 so that it would be parallel.
    (Is that true?)

    Anyways, I then converted the equation of the line out of parametric into (x-3)/2 = Y = -(Z-8).
    (I know that part's right.)

    But now I'm not sure what to do. Ideas?
  2. jcsd
  3. Jan 13, 2010 #2


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    Yes, your parallel plane equation is correct. Now just substitute x, y and z from the line equation into the plane equation and figure out what D must be.
  4. Jan 14, 2010 #3


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    It is, in fact, sufficient to use a single point on the line. Do you see why? For example, it should be easy to find D such that (3, 0, 8) (taking T= 0 in the equations of the line) is on the plane.
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