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Homework Help: Subtracting two vectors

  1. Jan 28, 2010 #1
    This is not a homework question, just a coursework reading.

    1. The problem statement, all variables and given/known data
    Please look at the figure on the right hand side


    2. Relevant equations
    R = A+B
    R = A - B

    3. The attempt at a solution

    So I tried to understand the concept of subtracting vectors.
    I want to do the adding convention instead of subtracting them.

    If I move A to connect to B (Tip Tail method), then I would have C (resultant) in an opposition direction (now going up from B to A).

    So I thought C = B+A, yet since the original problem is opposite direction, I say C = -(B+A)
    But that's wrong since C = A - B

    For the figure on the left hand. I can do the adding convention.
    Reverse the initial B to positive direction (dot line), and so C = A + B.
    Therefore, the actual answer is just C = A + (-B)

    Please help me to correct my misunderstanding with subtracting vector. I remember back in high school my teacher told me NEVER THINK ABOUT SUBTRACTING, DO ADDING.

    The reason I want to understand is that, if the question asks me "bases on the figure on the right hand, find C" I would be wrong
  2. jcsd
  3. Jan 28, 2010 #2


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    Why can't you apply the figure (a) to the problem (b)?
  4. Jan 28, 2010 #3

    Even if I move vector B freely to A (tip-tail), and I can't get -B

    In figure a I changed B from downward to upward.

  5. Jan 28, 2010 #4


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    If it's easier, first change the direction of vector B (in order to obtain -B), and then move it to A, respecting the rules of vector addition.
  6. Jan 28, 2010 #5
    But why do we need to change the direction when the question asks find R.
    Originally, B and A are in positive direction (up ward). So assuming B and A are free vectors, just as in figure A, I can move any vector til-tail.

    Since they are all upward, there is no reason why I need to reverse the direction of B.

    I mean let's not say "produce -B". When I see the problem "find R". I did that method and the answer is obvious wrong

    C = A - B
    4 = 6 - 2 =/ ||| 8 = 6+2 unless you are talking about the difference in units, then subtracting makes sense. But that's very confusing when it comes to a number in calculation unless A - B is stated.
  7. Jan 28, 2010 #6


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    Wait a minute, what exactly is your "R"?
  8. Jan 28, 2010 #7
    Oh Sorry. I meant C, the resultant.
  9. Jan 28, 2010 #8


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    Just to point out, the resultant is the vector which you get when you add a number of vectors. Since, when "subtracting", you only add opposite vectors, the sum is still a resultant. It's just a term for a sum. So, what exactly are you trying to do?
  10. Jan 28, 2010 #9

    Thanks. So if we look at figure b, let's assume it is a question.
    Find C.

    When I see this problem, I would first do tip-tail method, which is really adding vectors.
    So I move B to A.
    I find both upward direction, so A + B = C.
    Let A = 10, B = 15
    C = 25

    But now back to the reality. The original C was downward, but in ti-tail, I see C upward. Now I think it's okay since the magnitude is the same.

    But why would people do A - B in the first place?
  11. Jan 28, 2010 #10


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    If A = 10, and B = 15, C does not equal 25. Further on, C = A + B and C' = A - B have different magnitudes.
  12. Jan 28, 2010 #11
    Oh, I didn't realize C is longer than C'.

    IF the question says "Find C with original figure b"
    By looking at the picture, just because C is downward, we assume it has to be A - B?
  13. Jan 28, 2010 #12


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    We see C (in figure (b) ) equals A - B because the laws of vector addition (subtraction). It doesn't matter where it's pointing. You could rotate the whole picture by an amount, but C would still be equal to A - B.
  14. Jan 28, 2010 #13
    the laws of vector addition (subtraction)

    A - B = A + (-B)

    What I really don't understand is, why would we ever consider subtraction when the problem asks "find C"
    A + B = C
    Obviously A + B produces a longer C than A - B.
    Unless the problem says "A - B = ? " then I know how to do the math 10 - 5 = 5, so C = 5

    Where does -B coming from in figure b? Unless this -B comes from the original B in figure a, then it makes sense C is A - B since adding A + - B.

    But I am so confused when the figure b is its own original, assuming figure a never exist.
  15. Jan 28, 2010 #14


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    Do you understand that this does not hold (unless the vectors are paralell to each other)?
  16. Jan 28, 2010 #15
    The numbers are just there for "saying", not for real demonstration.
    But again,

    when the figure b is its own original, assuming figure a never exist, a - b will not exist, then finding c will just = a + b
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