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!

Prove that the distance between point-line is given by some formula

  1. Oct 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that if u is a vector from any point on a line to a point P not on the line, and v is a vector parallel to the line, then the distance between P and the line is given by

    NORM of u x v / NORM v

    u x v--> cross product of u and v


    I know how to calculate the distance between a point and a line, but I just dont know how to start proving this...

    any help please?

    thanks a lot
     
  2. jcsd
  3. Oct 14, 2011 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Well, you could start by working out what the vectors u and v are.
     
  4. Oct 14, 2011 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Do you need to formally prove this or is a picture showing it's true enough? It's pretty easy to show why it's true using a diagram.
     
  5. Oct 14, 2011 #4

    uart

    User Avatar
    Science Advisor

    Use u x v = |u| |v| cos(theta)
     
  6. Oct 14, 2011 #5

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You mean sin θ, right?
     
  7. Oct 14, 2011 #6

    yeah, its sinθ ... but I still don't quite get how to do it...

    And also, yes, I believe you have to prove it algebraically or something
     
  8. Oct 14, 2011 #7
    Ok, so we know that the norm of uxv is the area of the parallelogram formed by u and v...
    The norm of v has no geometric interpretation (its just the length of a line)

    How can we relate this so it gives the distance between P and the line...

    any more ideas??
     
  9. Oct 14, 2011 #8

    Mark44

    Staff: Mentor

    No and no. The norm of a vector v has a perfectly good geometric interpretation - it's the length of the vector. A line has infinite length - maybe you meant line segment?
     
  10. Oct 14, 2011 #9
    yeah, line segment. Anyway... I just don't know how to relate both of these.

    Is the norm of v considered the "base" of the parallelogram?
     
  11. Oct 14, 2011 #10

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Prove that the distance between point-line is given by some formula
Loading...