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Dot product

  1. Jun 8, 2006 #1
    so i have to determine the obtuse angle between the diagonals in the following diagram:


    this is what i have so far:

    let's call the intersection of the diagonals O
    so to find the obtuse angle, we can apply dot product (OW • OZ)

    |OW| = 1/2 |YW|
    = sqrt(61)/2

    |OZ| = 1/2 |XZ|
    = 3sqrt(24)/2

    but if cos (theta) = (OW • OZ)/ (|OW||OZ|)

    i don't have the numerator portion which is usually found with coordinates. so what do i do now?
  2. jcsd
  3. Jun 8, 2006 #2
    Why not choose a coordinate system that is convenient?
  4. Jun 8, 2006 #3
    oh ok so X = (0,0), W = (5,6), Z = (15,6), Y = (19,0)? and then go on to find the position vectors of OW and OZ?
  5. Jun 8, 2006 #4
    You could do it that way. It doesn't really make a difference as long as you can construct vectors OW and OZ (using your logic)
    Last edited by a moderator: Jun 8, 2006
  6. Jun 8, 2006 #5


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    You mean Y = (10,0), right?

    If you want the angle between the diagonals, then why not simply find the angle between the vectors (X,Z) and (Y,W)?
  7. Jun 8, 2006 #6
    yeah the Y coordinate was a typo. and i can see how your method is easier as well. i think the technique i chose is a little bit better to visualize, as you can actually see the diagonals intersecting and forming the obtuse angle.
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