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Homework Help: Dot product - Orthogonal

  1. Mar 9, 2010 #1
    By evaluating the dot product,

    find the values of the scalar s for which the two vectors
    b=X+sY and c=X-sY
    are orthogonal
    also explain your answers with a sketch:





    my working

    (X,sY).(X,-sY) has to equal 0 for them to be orthogonal

    x.x = 1 since they are unit vectors
    sY.-sY = -1 to make the whole thing 0

    s = 1
    1*y . -1*y = -1

    1-1 =0

    sketch would be two vectors perpendicular to one another?
     
  2. jcsd
  3. Mar 9, 2010 #2
    could someone please inform me If my work is correct?
    cheers
     
  4. Mar 9, 2010 #3

    Mark44

    Staff: Mentor

    (X + sY).(X - sY) = 0
    ==> X.X + sY.X - sX.Y -s2Y.Y = X.X - s2Y.Y = 0
    ==> 1 - s2 = 0

    You found one solution for s; there are two.
     
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