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More vector help (subtraction)

  1. Sep 16, 2007 #1


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    vector A = 7i + 4J
    vector B= -4i - 8j
    vector F = vector A - 3B

    are you allowed to do this:
    Fx= Ax - 3Bx : 7-3(-4) =19
    Fy= Ay -3By : 4- 3(-8) = 28
    or is there some rule to get the 3b?

    and then how do you get the direction? when i do tan^-1 (28/19) = 55.8 . but how can i tell what quadrant vector F is in? i know vector A is in quad 1. and B is in quad 3. but since i am subtracting vector B, it is really going in quad 1? so is vector F really in quad 1?
    sorry for all the questions!!
  2. jcsd
  3. Sep 16, 2007 #2
    Get some graph paper, and draw it! Draw A, B, -3B and F. Can you see what the numbers are actually representing as geometry?

    It should be obvious which quadrant things are in... if x and y are both positive, they're in the first quadrant... I'll let you fill in the conditions for the other three.
  4. Sep 16, 2007 #3


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    i did draw it already.
    i know A is in quad 1.
    B is in quad 3, but since i am subtracting ( i have to take the opposite vector) it would be in quad 1 as well.
    so vector F should be in quad 1 correct?
  5. Sep 16, 2007 #4
    Yes. You can also see it from the graph. Or, by noting that the defining of a vector in quadrant 1 is that both x and y components are positive. Can you generalise that definition for the other quadrants?
  6. Sep 16, 2007 #5


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    Homework Helper

    Your components look to be correct. You can calculate each component algebraically as you have done.

    Both components of F are positive, so what quadrant does that put it in?

    (I just spotted your later response. Your graph seems to confirm the algebra.)
  7. Sep 16, 2007 #6


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    ^thank you both! i just needed to make sure that you are allowed to find components like that. by multiplying the 3 with the B component. thanks!
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