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Math Help - Equation of plane from 2 lines

  1. #1
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    Equation of plane from 2 lines

    OK here is the question.

    Find an equation of the plane that contains the lines given by

    (x-1)/-2 = y = z+1

    and

    (x+1)/-2 = y-1 = z-2

    This is what I did.

    I found 2 points for the first line and 2 points for 2nd line

    A= (0 , 0.5, -0.5)
    B=(1 , 0 , 1)

    C= (0, 0.5, 1.5)
    D= (1, 0, 1)

    then i got their vector equations
    AB = <1, -0.5, 1.5>
    CD = <1, -0.5, -0.5>

    What now? Do i get their cross product? I did cross product, substituted it with a point on the plane, point A i think, and then got the equation x+2y = 1.

    But the answer doesnt seem right to me, so I would like some clarification as to whether I did anything wrong.
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  2. #2
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    Quote Originally Posted by adamantine View Post
    OK here is the question.

    Find an equation of the plane that contains the lines given by

    (x-1)/-2 = y = z+1

    and

    (x+1)/-2 = y-1 = z-2

    This is what I did.

    I found 2 points for the first line and 2 points for 2nd line

    A= (0 , 0.5, -0.5)
    B=(1 , 0 , 1)

    C= (0, 0.5, 1.5)
    D= (1, 0, 1)

    then i got their vector equations
    AB = <1, -0.5, 1.5>
    CD = <1, -0.5, -0.5>

    What now? Do i get their cross product? I did cross product, substituted it with a point on the plane, point A i think, and then got the equation x+2y = 1.

    But the answer doesnt seem right to me, so I would like some clarification as to whether I did anything wrong.

    It looks fine to me: it's easy to check that x+2y=1 contains both lines...

    Tonio
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