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Question about vectors and rectangles in R3

  1. Jan 22, 2012 #1
    Hi all, I was doing some review questions for my vectors test tomorrow and I have no idea how to even start this one. I hope any of you can help me :biggrin:

    1. The problem statement, all variables and given/known data
    The rectangle ABCD has vertices at A(-1,2,3), B(2,6,-9) and D(3,q,8).
    Note that the "q" in coordinate D is a variable

    a. Determine the coordinates of the vertex C
    This is the question im stuck on, no idea how to start. This question is in the dot/cross product section of the textbook, so I'm assuming we have to use either one to solve this problem:confused:

    b. Determine the angle between the two diagonals of this rectangle.
    Need the vertex C to figure out the diagonals...

    2. Relevant equations
    if a= (a1, a2, a3), b= (b1, b2, b3),

    a.b = a1*b1 + a2*b2 + a3*b3
    a.b = |a|*|b|*cosσ, where σ is the angle between a and b

    3. The attempt at a solution
    I found coordinate D to be (3, 14, 8) and am trying to use the fact that in this case, a.b = 0 because it is a rectangle and every side is perpendicular.

    Any help is appreciated, thanks!

    EDIT: Solved, I was just over-thinking it. Thanks anyways
    Last edited: Jan 22, 2012
  2. jcsd
  3. Jan 22, 2012 #2


    Staff: Mentor

    A comment on your use of the word "coordinate."

    D is a point, not a coordinate ("I found coordinate D ... "). What you did was to find the missing coordinate of point D.
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