1. Limited time only! Sign up for a free 30min personal 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!

Using Cross-Product and Vectors to find the distance between parallel lines ?

  1. Sep 11, 2011 #1
    Given the following two lines, prove that they are parallel, then find the distance between them...

    (I have circled in red the two parts of the answer which I don't understand. Namely, why are they using the cross-product here, doesn't that give you a value perpendicular to the lines, hence a new vector that is on the parallel planes of the lines? The second part I highlighted I have no idea why they chose this.)

    Could someone please explain the reasons to me? Something that I could visualize would be helpful.

    Thanks, prior!

    Distancebetweenparallellines.jpg
     
  2. jcsd
  3. Sep 11, 2011 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Remember the formula

    [tex]\| \vec{AP}\times\vec{AB}\| =\|\vec{AP}\|\|\vec{AB}\|\sin(\theta)[/tex]

    so your formula results in
    [tex]\|\vec{AP}\|\sin(\theta)[/tex]

    Draw a picture of two parallel lines and label A,P, and B and the angle θ between the vectors AP and AB. If you draw a perpendicular line between the vectors you will see that is its length by looking at the triangle with θ the angle between the two vectors.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Using Cross-Product and Vectors to find the distance between parallel lines ?
Loading...