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Finding a scalar such that vectors p and q are parallel

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data
    Let:
    p = (2,k)
    q = (3,5)
    Find k such that p and q are parallel

    3. The attempt at a solution

    Well, I know that for two vectors to be parallel we need to have p = kq.

    I know the answer will be kind of obvious but I just can't get it lolll, any help please??

    Thanks
     
  2. jcsd
  3. Oct 10, 2011 #2

    Mark44

    Staff: Mentor

    What does it mean for two vectors (p and kq, here) to be equal?
     
  4. Oct 11, 2011 #3
    Hummm.... They need to have the same magnitude and direction?
     
  5. Oct 11, 2011 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    (a, b) and (c, d) are parallel if and only if c/a= d/b.
     
  6. Oct 11, 2011 #5

    Mark44

    Staff: Mentor

    And what does this say about the coordinates of the two vectors?
     
  7. Oct 11, 2011 #6

    robphy

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    Science Advisor
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    Gold Member

    Thinking geometrically...

    HallsofIvy's statement (essentially a similar-triangles argument) is equivalent to requiring that the slopes are equal.
    Alternatively, consider certain "products" involving vectors and their geometric interpretation.
     
  8. Oct 11, 2011 #7
    That they must be equal also, I guess...

    So... p = tq (I'm using "t" as the scalar multiplying q):
    tq = 2/3 (3,5) = 2, 10/3

    So --> p = (2, k) = (2, 10/3)

    k = 10/3 ????

    Is that the way to do it? (trying to match the numbers only) or is there a more "pro" approach to it? lolll
     
  9. Oct 11, 2011 #8

    Mark44

    Staff: Mentor

    That's the answer you want.

    You can check your answer, by confirming that q = <3, 5> and p =<2, 10/3> are multiples of one another.
     
  10. Oct 12, 2011 #9
    great, thanks for the help!
     
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