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Convert equation of a line on a plane to R3 equation

  1. Apr 26, 2009 #1

    I have the equation of a plane P in R3.

    I have an equation f(x) of a line that exists on that plane, using an arbitrary origin/axis on the plane.

    I know the corresponding R3 coordinates of a point of f(x).

    Intuition tells me that I have all the info I need to calculate the equation to the line in R3, but I dont know exactly how.

    Any help appreciated.

  2. jcsd
  3. Apr 27, 2009 #2


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    Is the origin/axis for f(x) known in terms of R3 coordinates? If so then you don't need the R3 coordinates of a point of f(x).

    Alternatively if the origin/axis is not specified, then you need two points on the line. The plane equation is not needed.
  4. Apr 27, 2009 #3
    I have 3 points (in R3 coordinates) that the are on the function. It is aparabola, so I assume you need 3 points to construct.

    so taking into consideration what you said, i guess my question is now:

    how do you equation to a parabola in the form:


    from 3 points in R3?

  5. Apr 28, 2009 #4


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    In general you would need four points to determine a parabola. The general quadratic curve has six parameters, but these are unique only up to a constant multiplier, leaving five free parameters. Making it a parabola imposes one condition, reducing the number of free parameters to four.
    Last edited: Apr 28, 2009
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