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!

Unit Vector Perpendicular to a Triangle?

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

    Given: P=(1,-2,3), Q=(-4,2,5) and S=(2,1-4)

    Find a unit vector that is perpendicular to triangle PQS


    2. Relevant equations

    Cross and Dot Product

    3. The attempt at a solution


    Correct me if I'm doing wrong. I have two solutions that I've thought:

    1)What I would do is find the dot product of S and P and using that result, cross product with Q.

    or

    2)Find two dot products of two opposite triangle sidesand cross product on those.


    Just want to make sure I am doing right
     
  2. jcsd
  3. Sep 14, 2011 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If you take a dot product, you're left with a scalar. The cross product requires vectors to be calculated.

    You have the right idea of using the cross product though. One of the fundamental properties of the cross product is that [itex] v_1 \times v_2[/itex] is perpendicular to both v1 and v2. So you want to find two vectors from your triangle such that, if you get a vector perpendicular to both of them, you get a vector perpendicular to the triangle.
     
  4. Sep 14, 2011 #3
    I forgot that in dot product it gives you scalar result

    How about this then:

    I find P to S vector difference , which will result a vector of <-1, -3, -7> and using that vector, I cross product with Q
     
  5. Sep 14, 2011 #4

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    This is good. Taking the difference between S and P gives a vector that's pointing along one of the edges of the triangle, so is parallel to the triangle

    On the other hand, is Q parallel to the triangle?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Unit Vector Perpendicular to a Triangle?
  1. Perpendicular vector (Replies: 1)

  2. Vector Perpendicular (Replies: 2)

  3. Perpendicular Vectors (Replies: 5)

Loading...