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Math Help - Parallel Vectors

  1. #1
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    Parallel Vectors

    Hi,

    What does it exactly mean when vectors are parallel? There must be something that I do not understand because in the following question:

    "The line L is parallel to the z - axis . The point P has a position vector (8,1,0) and lies on L .

    Write down the equation of L in the for r = a +tb."

    I understand that a is the position vector and b is the direction, however no direction is directly stated. Apparently the answer for b is (0,0,1). So if the vector is parallel to the z axis why is the last number 1?

    I understand that in 3D vectors, it is in the form (x,y,z).

    Please explain!
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  2. #2
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    Two vectors are parallel if they are multiples of each other.
    <0,0,1>,~<0,0,-\pi>,~<0,0,12> are three parallel vectors.
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  3. #3
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    Thanks, so how would you know which vector out of the three parallel vectors to use?
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  4. #4
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    Quote Originally Posted by CSG18 View Post
    Thanks, so how would you know which vector out of the three parallel vectors to use?
    Any one of the three could be used.
    It is simply custom to use the first.
    It is custom to use these three as a basis for \mathcal{R}^3: <1,0,0>,~<0,1,0>,~<0,0,1>
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