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Homework Help: 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.


    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


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    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


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    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?
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