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Math Help - Use vectors to determine if points are @ right angle

  1. #1
    Super Member angel.white's Avatar
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    Use vectors to determine if points are @ right angle

    Use vectors to decide whether the triangle with vertices P(1,-3,2), Q(2,0,-4) and R(6,-2,-5) is right angled.


    I have a theorem in my book that says two vectors are orthogonal (perpendicular) if and only if their dot product is equal to zero. But I seem to be having difficulty turning them into vectors. Also, it seems that there should be 3 different sets of vectors that I could choose, how do I determine which are the best choice without graphing it out? ...and is there a method where that doesn't matter?
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  2. #2
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    Quote Originally Posted by angel.white View Post
    Use vectors to decide whether the triangle with vertices P(1,-3,2), Q(2,0,-4) and R(6,-2,-5) is right angled.


    I have a theorem in my book that says two vectors are orthogonal (perpendicular) if and only if their dot product is equal to zero. But I seem to be having difficulty turning them into vectors. Also, it seems that there should be 3 different sets of vectors that I could choose, how do I determine which are the best choice without graphing it out? ...and is there a method where that doesn't matter?
    You just need to form 3 separate vectors \vec{PQ}, \vec{QR}, and \vec{QP} by finding the displacements between the involved vectors in all 3 dimensions for example \vec{PQ}=(-1, 3, 6)and then you can just use the formula for finding Cross Products
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