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Finding the equation of a plane

  1. Sep 14, 2012 #1
    The question is in the paint doc.

    My solution:
    I created a matrix


    1. first row: 1,1,-1|2 which represents the equation of the plane x + y - z = 2
    second row: 2,-1,3|1 .... 2x - y + 3z = 1

    2. I came up with the parametric equation:

    x = 1 -2/3t
    y = 1 + 5/3t
    z=t

    3. The vector that represents this line is:
    <-2/3,5/3,0> = <-2,5,0>

    4. A point on the line is (1,1,0)

    5. <-1,2,1> - <1,1,0> = <-2,1,1> ... Vector // to plane Note: (-1,2,1) is a point on the plane.

    6. <-2,1,1> x <-2,5,0> = <5,2,8>

    7. 5(x-1) + 2(y-1) + z = 0
    or
    5x + 2y + z = 7

    The answer in the back of the book is: x - 2y + 4z = -1
     

    Attached Files:

  2. jcsd
  3. Sep 14, 2012 #2
    so am i on the wrong path??
     
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