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Math Help - Vectors

  1. #1
    Newbie VeronicaMarie's Avatar
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    Question Vectors

    How do i know if two vectors are parallel or orthogonal to each other?

    I know that if the dot product is equal to 0 the vectors are orthogonal to each other. but how do i know if a vector is parallel to one another or is neither parallel nor orthogonal?
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  2. #2
    MHF Contributor

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    Two vectors are parallel if one is a multiple of the other. The simplest way to test that is to divide the corresponding components of the two vectors and see if it is always the same: to test if <a, b, c> and <x, y, z> are parallel check if \frac{a}{x}= \frac{b}{y}= \frac{c}{z}.

    Also two vectors are parallel if and only if their dot product is equal to the product of the lengths of the two vectors.

    Two vectors are "neither parallel nor orthogonal " if neither of those is true- if the dot product is not 0 but also is not the product of the lengths of the two vectors.
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