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Satisfying the right hand rule

  1. Apr 13, 2008 #1
    1. The problem statement, all variables and given/known data

    Let a=(1,2,3) b=(-1,2,-1) and c=(0,1,-2). Do these vectors taken in this order, satisfy the right hand rule? Explain.


    3. The attempt at a solution

    I was told a cross b must equal c otherwise this is not satisfying? I'm VERY confused...can someone help out please and thanks?
     
  2. jcsd
  3. Apr 13, 2008 #2
    The cross product of a and b is perpendicular to both a and b.
    how can you tell if two vectors are perpendicular?
     
  4. Apr 13, 2008 #3
    Two vectors are perpendicular if the dot product is 0. So for example a cross b = c

    So then a dot c should equal 0 and the same should go for b dot c. So if both do equal zero it must mean they do satisfy the rule correct?

    EDIT: Ok nvm that does not help me out at all in my question.
     
    Last edited: Apr 13, 2008
  5. Apr 13, 2008 #4
    and if a dot c is not zero or b dot c is not zero, c cannot be the cross product of a and b.
     
  6. Apr 13, 2008 #5
    Hmm so how does the c=(0,1,-2) play a role in here?
     
  7. Apr 13, 2008 #6
    the fact that c=(0,1,-2) obviously plays a role in calculating the dot product of a and c or b and c.
     
  8. Apr 13, 2008 #7
    You don't have to take cross products, all you need is that they are linearly independent and they are.

    If you define the x-axis to point along a, y-axis to point along b and z-axis to point along c would your coordinate system be right handed? If so, then a-b-c in that order satisfies the right hand rule.
     
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