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Thread: 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,

    $\displaystyle OA=OB+BA$

    $\displaystyle OC=OB+BC$

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

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

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

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

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

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

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

    By (1) and (2);

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