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Homework Help: Two coplanar lines and finding the equation

  1. Mar 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Two coplanar lines, a and b are perpendicular to each other. a passes through the points (3,2,3) and (8,10,6). Find the equation for b if it passes through the point (7,49,25).

    2. Relevant equations
    The equation were trying to find is r = [x,y,z] + s [x1,y1,z1] + t [x2,y2,z2]

    3. The attempt at a solution
    Basically since the coordinates are perpendicular I used the cross product to find one direction vector. For my position vector I used (3,2,3). Now I'm not sure what to do with the last point (7,49,25) or what to do to find my second direction vector. I'm not even sure if I did the first part right. Help would be appreciated thanks!
  2. jcsd
  3. Mar 15, 2012 #2


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    Staff: Mentor

    Hi gundamshadow, Welcome to PF.

    Your question, being mathematical in nature, would probably fair better in the Precalculus forum. But I can give you a hint or two here :smile:

    The lines involved are said to be coplanar, and that plane must have a normal. A plane's normal has some nice properties involving vectors in the plane and cross and dot products. You might want to look into that :wink:

    You might start by finding any two vectors in the plane from the given points...
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