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Equation of a line

  1. Nov 29, 2006 #1
    1. The problem statement, all variables and given/known data

    I need to find the equation for the line that passes through the pont (-1, 2, -3) in the direction of the vector (1,-1,-1)

    2. Relevant equations

    The equation needs to be in the form v(t)=v subscript 0 + tv

    3. The attempt at a solution
    I know how to find the equation of a line passing through two points, but I have no idea how to find the equation with only one point heading in the direction of a vector. I'm not really looking for the answer, I'm looking for an explanation on how to find the equation of a line given one point in the direction of a vector. Any help would be appreciated. Thank you.

    I think I've found the solution, but I'm not sure. v=(1,-1,-1) and V subscript 0 = (-1,2,-3), therefore the equation of the line is (-1,2,-3) + t(1,-1,-1). Is this right?
    Last edited: Nov 29, 2006
  2. jcsd
  3. Nov 29, 2006 #2
    Take a look at dot products and cross products.
  4. Nov 29, 2006 #3


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    Staff: Mentor

    I'm not sure if your answer is correct, but one way to check it is to use what you already know -- how to find the equation based on two points. Since the line is in the direction of (1,-1,-1) from point (-1,2,-3), then a 2nd point on the line would just be (1,-1,-1) away from the first point, right?
  5. Nov 29, 2006 #4
    Thank you. I guess this question isn't that difficult. For some reason I thought it was harder than it was. :blushing: Thank you guys.
  6. Nov 30, 2006 #5


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    Staff Emeritus
    Science Advisor

    Actually, after the very good response to the "eigenvalue" question, yes, you should be embarrased!:smile:
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