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Scalar Equation of Plane Determining the value of k

  1. Apr 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2 + 5t, z = k is parallel to the plane with equation 4x + 3y – 3z -12 = 0.

    2. Relevant equations



    3. The attempt at a solution

    let k=a + bt

    x=2+3t
    y=-2+5t
    z=a+bt

    direction vector= (3,5,b)

    The normal to the equation 4x + 3y – 3z -12 = 0 is n=(4,3,-3)

    Dot product of the direction vector and normal: (4,3,-3).(3,5,6)=0
    12+15-3b=0
    b=9
    therefore z=a+9t

    So:

    x=2+3t
    y=-2+5t
    z=a+9t

    not sure where to go from here

    Thanks for any help!
     
  2. jcsd
  3. Apr 17, 2012 #2
    The line you got is parallel to the plane for any value of a, maybe except the one where this line is on the plane (that seems to be when a=10/3). There is nothing wrong here.
     
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