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!

Vector distance formula

  1. Jul 25, 2007 #1
    let P be a point NOT on line L that passes through points Q and R.

    [tex] \vec{A} = QR[/tex]

    [tex]\vec{B} = QP [/tex]

    prove that distance from point P to anywhere on line L is
    [tex] d = |\vec{A} x \vec{B}| divided by |\vec{A}| [/tex]

    so, i've tried doing the cross product after assigning variables for the A and B components. I ended up with a very tedious long multiplication of several variables, and I was wondering if there is an easier way to prove this formula.
     
    Last edited: Jul 25, 2007
  2. jcsd
  3. Jul 25, 2007 #2
    Draw a picture of what is going on and note that |AxB| is the area of the parallelogram generated by A and B. It's also equal to |A||B|Sin(t) where t is the angle between A and B.
     
  4. Jul 25, 2007 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Of course the shortest distance from P to a line is along the line through P perpendicular to the line. You might start by finding the equation of a line through P perpendicular to [itex]\vec{QR}[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?