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!

Vector proof question

  1. Apr 20, 2006 #1
    Okay, so I have a triagle with vertices A, B, and C.
    I know that the centroid, G, is where all the medians of the triangle intersect, and G divides the median at a 2:1 ratio

    Assuming point O is a point that's not on the triangle, how can I prove:
    OG = 1/3(OA + OB + OC) ?

    I've seen this equation a lot of times, but I'd like to see a proof of it for interest sake

    Thanks
     
  2. jcsd
  3. Apr 21, 2006 #2

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    Let [itex]P[/itex] be the midpoint of [itex]\overline{BC}[/tex]. Then:

    [tex]\overline{OB} + \frac{1}{2}\overline{BC} = \overline{OP}[/tex]

    [tex]\overline{OB} + \overline{BC} = \overline{OC}[/tex]

    [tex]\overline{OP} + \overline{PA} = \overline{OA}[/tex]

    [tex]\overline{OP} + \frac{1}{3}\overline{PA} = \overline{OG}[/tex]

    The last line comes from the fact that G divides the median [itex]\overline{PA}[/itex] at a 2:1 ratio. You should be able to figure it out from here.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Vector proof question Date
Vector Notation in Nolting Theoretical Physics 1 Mar 12, 2018
Vector Proof Centroid Theorem Jun 17, 2008
Another vector proof Sep 5, 2005
Vector Proof Jun 2, 2005
Vector Proofs in geometry Dec 10, 2003