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Lin Alg Question: Cross-Product Proof

  1. Oct 1, 2009 #1
    http://imgur.com/mceBq" [Broken]

    I'm curious to see if my conclusion is correct.

    thanks in advance.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 1, 2009 #2

    CompuChip

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    I don't really agree with your claim that if for two vectors a (non-zero) and b, axb = 0, then b = 0.
     
  4. Oct 1, 2009 #3

    Mark44

    Staff: Mentor

    Following up with what CompuChip said, what is a X 2a?
     
  5. Oct 1, 2009 #4
    I'm not sure why you don't agree. I end up with the statement:

    a X (b - c) = 0

    And for that statement to hold, the following must necessarily be true:

    b - c = 0

    since we know that a is nonzero.

    a is parallel to 2a, so taking the cross-product of two parallel vectors yields the zero vector, because there are an infinite number of vectors perpendicular to a single line.


    Sorry, but I don't seem to be following the logic you are trying to lead me through.
     
  6. Oct 1, 2009 #5

    HallsofIvy

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    The logic he is trying to lead you through is: Since, as you say, the cross product of two parallel vectors is 0, it does NOT follow that is [itex]u\times v= 0[/itex] then either u or v must be 0! In particular, if a is not the 0 vector, then neither is 2a but, again, [itex]a\times 2a= 0[/itex].

    If [itex]a\times (b- c)= 0[/itex] then the best you can say is that b- c is parallel to a: that is, that b- c is a multiple of a.
     
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