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Adding & Subtracting vectors

  1. Oct 27, 2012 #1
    1. The problem statement, all variables and given/known data
    If two collinear vectors [itex]\vec{A}[/itex] and [itex]\vec{B}[/itex] are added, the resultant has a magnitude equal to 4.0. If [itex]\vec{B}[/itex] is subtracted from [itex]\vec{A}[/itex], the resultant has a magnitude equal to 8.0. What is the magnitude of [itex]\vec{B}[/itex] ?


    2. Relevant equations

    None.



    3. The attempt at a solution

    |A| + |B| = 4.0 (1)
    |A| - |B| = 8.0 (2)
    sum the two equations :
    2|A| = 12
    => |A| = 6.0
    substitute in (1) :
    6.0 + |B| = 4.0
    => |B| = -2

    ====================
    is this a complete and right solution??
    should I draw the vectors??
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 27, 2012 #2

    haruspex

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    Clearly that's wrong since |B| cannot be negative.
    Let's step back a bit. They're added as vectors:
    |A+B| = 4
    |A-B| = 8
    Since they're collinear, you have equated |A+B| to |A|+|B| etc., but there is another possibility. Can you see what it is?
     
  4. Oct 27, 2012 #3
    Thanks haruspex

    so the solution :

    |A+B| = 4
    |A-B| = 8
    because they're collinear :
    |A| + |B| = 4
    |A| - |B| = 8
    sum the two equations :
    2|A| = 12
    |A| = 6
    substitute :
    6 + |B| = 4
    => |B| = ???

    do you mean by drawing??
     
  5. Oct 28, 2012 #4

    haruspex

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    No, you're still making an assumption that's wrong. What if A and B are in opposite directions?
     
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