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Math Help - Perpendicular Vector

  1. #1
    Junior Member NAPA55's Avatar
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    Perpendicular Vector

    If I'm given an algebraic vector as an ordered triple (1, 2, 3) and that's it, how would I go about finding vectors that are perpendicular to this one?

    I need to use the dot product.

    My book didn't show examples of such a problem, so I'm not sure how to do it.

    Thanks.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by NAPA55 View Post
    If I'm given an algebraic vector as an ordered triple (1, 2, 3) and that's it, how would I go about finding vectors that are perpendicular to this one?

    I need to use the dot product.

    My book didn't show examples of such a problem, so I'm not sure how to do it.

    Thanks.
    let (a,b,c) be perpendicular to (1,2,3)

    Since they are perpendicular their dot product must be zero

    (a,b,c) \cdot (1,2,3)=0  \to a+2b+3c=0

    now we need to solve this underdetermined system of equations.

    let c=s b=t then a=-2t-3s

    so we get the vector (-2t-3s,t,s)=(-2t,t,0)+(-3s,0,s)=

    t(-2,1,0)+s(-3,0,1)

    This is all of the vectors perpendicular to (1,2,3)

    they work for all values of s and t.

    I hope this helps.

    Good luck.
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