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Thread: Mutually perpendicular vectors

  1. #1
    Junior Member
    Mar 2011

    Mutually perpendicular vectors

    "Verify that if a and b are vectors of the same length then
    a + b and a - b
    are mutually perpendicular."

    How are you able to figure out how to verify that the vectors are the same length/mutually perpendicular? I know that you use the dot product, so (B]a[/B] + b) (a - b) to verify it although, I just do not understand why. How does the dot product of both vectors mean that they are of the same length/mutually perpendicular?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Nov 2010
    Madrid, Spain
    $\displaystyle (a+b)\cdot{(a-b)}= a\cdot a+b\cdot a-a\cdot b-b\cdot b$

    Now use

    $\displaystyle x\cdot x= \left\|{x}\right\|^2$ .
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