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Math Help - Dot Product and parallel

  1. #1
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    Dot Product and parallel

    u=i+j v=ai-j they are parallel and I need to solve for a

    I have no idea how to do it and any help would be greatly appriciated
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  2. #2
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    Parallel vectors are multiples of each other.
    Does a = -1 work?
    WHY?
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  3. #3
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    thanks a lot .

    i see that it works because then you have 2=-2, but i don't understand how you get it...
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  4. #4
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    Quote Originally Posted by carly_1026 View Post
    thanks a lot .

    i see that it works because then you have 2=-2, but i don't understand how you get it...
    Two vectors \vec u and \vec v are collinear (vulgo parallel) if

    k \cdot \vec u = \vec v~,~k \in \mathbb{R}

    Therefore:

    k \cdot (i + j) = ai - j~\iff~ ki +kj = ai -j~\iff~ ki = ai\  \wedge \  kj = -j

    From the last equation you get:

    k = -1 . Plug in this value into the equation ki = ai and you'll get a = -1
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