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Two coplanar lines and finding the equation

  1. Mar 16, 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!

    EDIT: I originally posted this in a different section but somebody told me it'd be better if I post it here. So if a mod could remove the other thread in the physics section that'd be awesome.
     
  2. jcsd
  3. Mar 16, 2012 #2

    tiny-tim

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    welcome to pf!

    hi gundamshadow! welcome to pf! :smile:

    have you drawn this?

    you have three known points, B C and D, and you want the line through B perpendicular to CD :wink:
     
  4. Mar 16, 2012 #3
    Thank you for the welcome :)

    So I'm assuming B is (3,2,3) and C is (8,10,6) etc.
    In that case how would I go about finding direction vectors if they're perpendicular? Is it a combination of cross product of B and C?

    EDIT: Also the term coplanar, does that mean the vectors in the equation have to be a multiple?
     
  5. Mar 16, 2012 #4

    tiny-tim

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    come on! :rolleyes:

    it's a simple triangle question! :smile:

    (you can use parallel lines, and cross products :wink:)

    (coplanar means in the same plane … any vector in it will be a linear sum of any two distinct vectors in it)
     
  6. Mar 16, 2012 #5
    I`m sorry Im really lost now. I subtracted (3,2,3) and (8,10,6) and got (5,8,3). So that is my position vector I hope.

    So as it stands the equation is r= (5,8,3) + s (xyz) + t (xyz)

    How do I get the other coordinates for vector s and t
     
  7. Mar 16, 2012 #6

    tiny-tim

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    hi gundamshadow! :smile:
    yes, that's the direction of your line CD

    so what is the line through B parallel to that?
     
  8. Mar 16, 2012 #7
    I thought that was the position vectorÉ And if its parallel does that mean that CD dot product by (7,49,25) will be zeroÉ
     
  9. Mar 16, 2012 #8

    tiny-tim

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    you've lost me :confused:

    what is the line through B parallel to CD?
     
  10. Mar 16, 2012 #9
    Im kinda lost too. And I got (0,-3,8)
     
  11. Mar 16, 2012 #10
    EDIT: Realised bumping not allowed. Please delete post. Sorry!
     
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