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Cross Product of Vectors

  1. Dec 14, 2013 #1
    True or False, if AxB = AxC then either A=0 or B=C.

    A, B, and C are vectors and I thought this statement would be true. However the answer key says it is not. Why?
     
  2. jcsd
  3. Dec 14, 2013 #2
    This can be explained by following example

    1387076046331.jpg
     
  4. Dec 14, 2013 #3
    Ok that makes sense. Now if the the magnitude of the cross product was not zero then B would have to equal C Right?
     
  5. Dec 14, 2013 #4
    The magnitude of AxB is equal to the magnitude of A times the magnitude of B times the sine of the angle between the vectors A and B. If the magnitude of C is larger than the magnitude of B, but the sine of the angle between A and C is less, AxC can be equal to AxB.
     
  6. Dec 14, 2013 #5

    D H

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    Not at all. All that AxB=AxC says is that either A=0 (in which case any two vectors B and C satisfy AxB=AxC), or that the components of B and C normal to A are equal.
     
  7. Dec 14, 2013 #6

    Dick

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    Or that since AxB=AxC is the same as AxB-AxC=Ax(B-C)=0 then A and B-C are parallel.
     
    Last edited: Dec 14, 2013
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