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Math Help - Parametric equation of lin eof intersection of two planes?

  1. #1
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    Question Parametric equation of lin eof intersection of two planes?

    Hi , I am doing this linear algebra question:
    Find the parametric equations of the line of intersection of the planes x+2z=0 and 2x-3y+4
    I don't know whether I am approaching this the correct way or if my answer is correct. What I did was found the cross product of the normals of the vectors which gave me (3,2,-3); then I subbed in zero for x to get 2z=0, -3y=4-> z=0, y=-4/3 and got the equation of the line as being L= (0,0,-4/3)+t(3,2,-3)
    Any feedback would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by macduff View Post
    Hi , I am doing this linear algebra question:
    Find the parametric equations of the line of intersection of the planes x+2z=0 and 2x-3y+4
    I don't know whether I am approaching this the correct way or if my answer is correct. What I did was found the cross product of the normals of the vectors which gave me (3,2,-3); then I subbed in zero for x to get 2z=0, -3y=4-> z=0, y=-4/3 and got the equation of the line as being L= (0,0,-4/3)+t(3,2,-3)
    Any feedback would be greatly appreciated.
    I'd just solve

    x + 2z = 0 .... (1)

    2x - 3y = 4 .... (2)

    simultaneously:

    Let x = t. Then y = (2t - 4)/3 and z = -t/2. This is the parametric equation of a line.

    Your solution is not consistent with mine eg. My line does not pass through (0, 0, -4/3) but yours does (in fact, that point does not even lie in the second plane ....)
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  3. #3
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    Thanks

    Thankyou so much your way definitely makes more sense and is easier :P
    Quote Originally Posted by mr fantastic View Post
    I'd just solve

    x + 2z = 0 .... (1)

    2x - 3y = 4 .... (2)

    simultaneously:

    Let x = t. Then y = (2t - 4)/3 and z = -t/2. This is the parametric equation of a line.

    Your solution is not consistent with mine eg. My line does not pass through (0, 0, -4/3) but yours does (in fact, that point does not even lie in the second plane ....)
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