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Math Help - The art of making vectors parallell

  1. #1
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    The art of making vectors parallell

    Find a number a so that the vectors (a,2+a,6) and (2,1,-3) are parallell.
    How do I do that?
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  2. #2
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    Quote Originally Posted by a4swe View Post
    Find a number a so that the vectors (a,2+a,6) and (2,1,-3) are parallel.
    Two vectors are parallel if they are non-zero multiples of each other.
    (a,2+a,6)=t(2,1,-3)=(2t,t,-3t)
    Thus t=-2. a=?
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  3. #3
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    Quote Originally Posted by a4swe View Post
    Find a number a so that the vectors (a,2+a,6) and (2,1,-3) are parallell.
    How do I do that?
    Also if and only if their dot product is zero.
    The dot product in this case is,
    2a+(2+a)1+6(-3)=0
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  4. #4
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    Quote Originally Posted by ThePerfectHacker View Post
    Also if and only if their dot product is zero.
    No, if their dot product is zero then they are perpendicular not parallel.
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  5. #5
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    Quote Originally Posted by Plato View Post
    No, if their dot product is zero then they are perpendicular not parallel.
    Thank you Plato.
    ---
    I meant if their cross product is a zero vector.
    But that seems more complicated than finding scalar multiples.
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  6. #6
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    Thanks.
    But can I say anything about parallelity considering the soultion set of some particullar linear equation system?

    And Plato, what you said is equavilent with: "Two vectors are parallell if they are linear dependent" right?
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  7. #7
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    I am almost afraid to answer not really understanding the question.
    But yes two parallel vectors are linearly dependent.
    I do not understand what you mean by ‘system’.
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  8. #8
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    By system I mean a collection of two or more equations.
    But that was another question.
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  9. #9
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    And just now I realized that my first question in my second post was a stupid one, problem completly solved, thank you Plato.
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