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Math Help - Vector proof

  1. #1
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    Vector proof

    Using vectors and vector rules i need to prove that OA.OC=OB.OD given ABCD is a rectangle and O (origin) is on a different plane.

    ive let OA = a, OB = b etc and drawn a diagram. Im not very good at vector proofs and dont know how to tackle the problem.
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  2. #2
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    Quote Originally Posted by kumquat View Post
    Using vectors and vector rules i need to prove that OA.OC=OB.OD given ABCD is a rectangle and O (origin) is on a different plane.

    ive let OA = a, OB = b etc and drawn a diagram. Im not very good at vector proofs and dont know how to tackle the problem.
    Dear kumquat,

    OA=OB+BA

    OC=OB+BC

    OA.OC=\left(OB+BA\right).\left(OB+BC\right)

    \Rightarrow OA.OC=OB^2+OB.BC+OB.BA+BA.BC

    Since, A\hat{B}C=90^{0}\Rightarrow BA.BC=0}

    \Rightarrow OA.OC=OB^2+OB.BC+OB.BA------------(1)

    OB.OD=OB.\left(OB+BC+CD\right)

    \Rightarrow OB.OD=OB.\left(OB+BC+BA\right)

    \Rightarrow OB.OD=OB^2+OB.BC}+OB.BA-------------(2)

    By (1) and (2);

    OA.OC=OB.OD
    Last edited by Sudharaka; May 12th 2011 at 08:50 AM.
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