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Two vectors are parallel if their cross product is 0?

  1. Feb 29, 2008 #1
    the question is:

    u = 9i-6j
    and
    v = 5i+bj

    for what value of b would u-v point in the same direction as w = 7i-3j?

    can anyone help me get started on this problem, im not looking for answers just a little bit of help because i'm confused.. thanks
     
  2. jcsd
  3. Feb 29, 2008 #2

    Dick

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    There's no 'b' in your problem statement. What is it?
     
  4. Feb 29, 2008 #3
    Dick, the b is in the v component. I missed it at first glance too.
    Anyway teffy, what conditions do you know that tests if two vectors are parallel?
     
  5. Feb 29, 2008 #4
    v=5i + bj

    thats where the b is..
     
  6. Feb 29, 2008 #5

    Dick

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    Ooops. Missed it. So u-v=4i+(-6-b)j. Now answer arunbg's question.
     
  7. Feb 29, 2008 #6
    um that two vectors are parallel if their cross product is 0?...
     
  8. Feb 29, 2008 #7
    So what do you get when you take the cross product?
     
  9. Feb 29, 2008 #8
    i think thats where my problem lies now...im not sure how to find that out.
     
  10. Feb 29, 2008 #9

    Dick

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    That's one way. But in only really works in three dimensions. More generally vectors A and B point in the same direction if A=k*B for some k>0 (any nonzero k if you don't mind them pointing in opposite directions). So you could set the ratio of the components equal.
     
  11. Feb 29, 2008 #10
    okay so then how do i find the value of b?
     
  12. Feb 29, 2008 #11

    Dick

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    Write down expressions for the ratio of the i components and the ratio of the j components and set them equal.
     
  13. Feb 29, 2008 #12

    tiny-tim

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    Pictures often help with vectors!

    (Cross-product will work, but, as you've found out, it's not particularly easy:yuck:, and there is a simpler way)

    If you're stuck, it often helps to draw a picture. :smile:

    You did head this as a vectors problem, rather than an algebra one.

    So draw (only roughly) the two vectors you have to make parallel!

    What trigonometric thing could you measue to check if they're parallel?
     
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