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Homework Help: Parallel vectors

  1. Jul 10, 2012 #1
    Reading through a book and this question popped up, but the question didn't actually cover parallel vectors so i'm not sure what to make of it:

    Given that c = 3i + 4j and d = i -2j find

    t if d-tc is parallel to -2i + 3j

    I done d - tc and got (1-3t)i + (-2-4t)j but i'm not quite sure how to equate this to the parallel vector -2i + 3j

    in the solutions for some reason they have done the coefficient of i in vector -2i + 3j and multiplied it by the coeffecient of j in d-tc and done the same for j, so they have

    -2(-2-4t) = 3(1-3t)

    but I don't really know how they got that, if anyone could explain thanks.
  2. jcsd
  3. Jul 10, 2012 #2
    If two vectors are parallel, what can you say about the coefficients of i and j ?
  4. Jul 10, 2012 #3
    I have no idea

    edit: searched around and if two vectors are parallel then one of them is multiplied by a scalar, so

    (1-3t)i + (-2-4t)j = k[-2i+3j]

    so 1-3t = -2k , -2-4t = 3k

    k = (1-3t)/-2

    -2-4t = 3((1-3t)/-2)
    t = -1/17
    Last edited: Jul 10, 2012
  5. Jul 10, 2012 #4
    Right! :smile:

    Alternatively, you could say that they have the same "slope", so

    (-2-4t) / (1-3t) = 3 / (-2)

    ie the ratio of the i and j coefficients are the same.

    (One has to be careful if one of the coefficients is zero, though.)
  6. Jul 10, 2012 #5
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