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Can some explain vector a+b must be great than a-b

  1. May 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Can some explain vector a+b must be great than a-b

    2. Relevant equations
    none this is conceptual

    3. The attempt at a solution
    I believe this is false because the direction can be + or -. can you explain to your thoughts
     
  2. jcsd
  3. May 24, 2016 #2

    berkeman

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    Staff: Mentor

    It is certainly not true in general (not even for scalars). You would need to constrain a and b more to have something that was true.
     
  4. May 24, 2016 #3
    i think one should try checking the contention that addition of two vectors must be greater than subtraction - as it is true in case of scalars.

    as vectors are having magnitude as well as direction -their addition and subtraction will result into a vector and its magnitude and direction will depend on the angular relation between them -
    suppose the angle between them is 180 degree-then their addition will give you a vector which is smaller than the magnitude of a vector when you subtract one from another.

    however if the angle between them is zero their addition will give you a vector larger than the result after taking a difference.
    you can try taking an arbitrary angle between them and find the conditions for which the 'contention' holds or does not hold.
     
  5. May 24, 2016 #4

    berkeman

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    Staff: Mentor

    Is it? Not unless you constrain it to positive scalars...
     
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