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Homework Help: Line of intersection of Two Planes

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data

    Please disregard, sign error corrected in the cross product

    Determiner the line of intersection of the following two planes. Write the parametric equations for this line.


    2. Relevant equations

    3. The attempt at a solution
    First I crossed my normal vectors from the given equations: (2,1,-2)cross(3,-6,-2)= (-14,-2,15)

    Then I solved my simultaneous equations starting with y=0, which gave me x=10 and z= (15/2).

    To get into the parametric equation I took the point (10,0,15/2) + t(-14,-2,15), which gave me

    Viewing this data in calcplot 3d shows that my line of intersection is no where near my planes.
    Last edited: Feb 20, 2013
  2. jcsd
  3. Feb 20, 2013 #2
    Error found in cross product (-14,-2,-15). Problem solved.
  4. Feb 21, 2013 #3


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    Science Advisor

    I'm not sure why you took the cross product of the normal vectors. Simply subtracting the first equation from the second eliminates z and gives x- 7y= 5.
    That is, x= 7y+ 5 and putting that back into the first equation, 2x+y-2z= 2(7y+ 5)+ y- 2z= 15y+ 10- 2z= 5. 2z= 15y+ 5.

    Parametric equations for the line of intersection are x= 7t+ 5, y= t, z= (15t+ 5)/2.
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