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Homework Help: Determine the values of a and c on a line.

  1. Apr 26, 2007 #1
    A line is defined by the equations x = 3-4t, y = 8t, and z = 6+t

    a) Determine the vector and symmetric equations of the line

    b) Determine the values of a and c if the point (a, 2, c) lies on the line.

    I have part a) solved: (x,y,z) = (3,0,6) +t(-4,8,1)

    (3-x)/4 = y/8 = z-6/1

    I am a little unclear has to how I would solve for a and c though in part b)

    y-2/8 = a-x/4 = z-c/1 but I am not sure where to go from there...
     
  2. jcsd
  3. Apr 26, 2007 #2

    NateTG

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    At the point [tex](a,2,c)[/tex], what is the value of y?
     
  4. Apr 26, 2007 #3
    y = 2, so 2/8 = 1/4

    therefore, 3-x/4 = z-6/1 = 1/4

    (2, 2, 25/4) I think I got it. Thanks
     
    Last edited: Apr 26, 2007
  5. Apr 27, 2007 #4

    VietDao29

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    Yup. Correct. Or you can also use its parametric equation to solve the problem.
    When y = 2, that means 8t = 2 ~~> t = 1 / 4
    Sub t = 1 / 4 in x, and z, we have:
    [tex]x = 3 - 4t = 3 - 4 \times \frac{1}{4} = 2[/tex]
    [tex]z = 6 + t = 6 + \frac{1}{4} = \frac{25}{4}[/tex], so the coordinate of the point is:
    [tex]\left( 2; \ 2 ; \ \frac{25}{4} \right)[/tex], so a = 2, and c = 25/4.
     
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