1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A basic question about vectors

  1. Nov 11, 2009 #1
    I've found this regular definition of vectors: A quantity which has both magnitude and direction.

    On some sites, I've also found the addition: They satisfy the vector laws of addition (commutative, associative, distributive).

    Is it really necessary that all vectors should satisfy all those laws? Are there any exceptions?
  2. jcsd
  3. Nov 12, 2009 #2
    Yes and no respectively. Otherwise it wouldn't be a vector!
    There are other things that are similar to vectors, but we give them different names (like scalars and stuff).
  4. Nov 12, 2009 #3

    The "magnitude and direction" definition is an intuitive one. They make a lot of sense for R^n, but for some vector spaces, it doesn't. There are function vector spaces, where we create rules for adding and scaling functions. For example, if f(x) = x^2 and g(x) = x + 1, then (f + g)(x) = x^2 + x + 1. But what "direction" does f, g, or f+g point? It's much more abstract!
  5. Nov 13, 2009 #4
    Thanks for your replies and sorry about my late reply.

    I was also wondering - current is neither a scalar nor a vector, right? But we say "current flows from A to B", which specifies a direction right? So it should be a vector....

    And also, if it is neither, then which category does it fall in?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook