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Planes in 3 space

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data
    find the point of intersection of the lines x=2t+1, y=3t+2, z=4t+3 and x=s+2, y=2s+4, z=-4s-1
    then find the plane determined by these lines


    2. Relevant equations



    3. The attempt at a solution
    i have no idea how to find the point of intersection for those two lines
    but i figured that im going to need that in order to find the plane, since ill need a point and the normal vector to find the plane, and i can just find the normal vector by using the cross product on the two vectors that are parallel to the lines
    but im stuck on the very first part, how do i find the intersection?
     
  2. jcsd
  3. Dec 4, 2011 #2

    Dick

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    Since 2t+1=x and s+2=x you can say that 2t+1=s+2. Can you see what to do now?
     
  4. Dec 4, 2011 #3
    solve for one of the variables?
     
  5. Dec 4, 2011 #4

    Dick

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    Sure. You can use y and z to make two more equations. Solve them for t and s. You've got three equations in the two unknowns s and t.
     
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