1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Varying Forms for an Equation of a Line in R^3

  1. Oct 17, 2015 #1
    I was doing some course work earlier today and noticed that I've seen two different equations for a line in 3D space. Usually the equation I use is:
    [itex]\vec r(t)=<x_{0}, y_{0}, z_{0}> + t<x, y, z>[/itex]
    You plug in the various points with what the problem provides. However, a few times I have seen a problem that uses the equation:
    [itex]\vec r(t)=<x_{0}, y_{0}, z_{0}> + t<x-x_{0}, y-y_{0}, z-z_{0}>[/itex]

    How do I know which equation to use? Or are these equivalent?

    Thanks!
     
  2. jcsd
  3. Oct 17, 2015 #2
    You can define a line either with 1 point and a directing vector, or with 2 points.
    The first form of is the definition of a line passing through ##M_0 = (x_0,y_0,z_0)## and directed by ##\vec u = (x,y,z)##, while the second form is the definition of a line passing through ##M_0 ## and ##M = (x,y,z) ## (directed by ##\vec{ M_0M}##)
     
  4. Oct 17, 2015 #3
    Oh, that makes perfect sense. Thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Varying Forms for an Equation of a Line in R^3
  1. Lines in R^3 space (Replies: 7)

Loading...