Coplanar vectors

  1. Two free vectors are always coplanar.

    Then if A and B are free vectors, are A, B, and A+B all coplanar in all cases?
     
  2. jcsd
  3. Mark44

    Staff: Mentor

    Yes.
    Any two vectors that start from the same point (you can assume that they start from the origin) determine a plane. Any linear combination of these vectors (including 1*A + 1*B) also lies in that same plane.
     
  4. Cool.

    How about this:

    If two vectors are linearly dependent, they are collinear. They are always coplanar.

    If three vectors are linearly dependent, they are coplanar. Three vectors are always all co"cubeular" (I don't know a word like coplanar for a three dimensional object.)

    Based on this pattern, it correct to say that:

    If n vectors are linearly dependent, then they are co(n-1 space object) and are always co(n space object).

    Since for two vectors, an n-1 space object is a line, for three it is a plane, and so on.

    Am I making sense?
     
    Last edited: Aug 28, 2012
  5. Mark44

    Staff: Mentor

    Yes. If two vectors are linearly dependent, then each is a nonzero scalar multiple of the other.
    They could be collinear, depending on which vectors we're talking about.
    I don't believe there is any special terminalogy beyond coplanar.
    Yes, I get what you're saying, but as I said, I don't believe there is any terminology beyond coplanar.
     
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