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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.

    2x+y-2z=5
    3x-6y-2z=15

    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
    x=10-14t
    y=-2t
    z=15t+(15/2)

    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

    HallsofIvy

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    Staff Emeritus
    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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