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Homework Help: Help with physics demonstration

  1. Oct 16, 2005 #1
    Hi ,
    Please can I have some help with this demonstration:
    Let a#0 ( #= different)
    Show that if a x b = a x c and a.b=a.c, then b=c ( Hint: Cross both sides of the first equation with a)
    When I cross by a ( as the hint suggests) , I found 0=0 ??
    thank you
  2. jcsd
  3. Oct 16, 2005 #2


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    What is "a x b" vs. "a.b"?
  4. Oct 16, 2005 #3


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    What are your definitions of The dot and cross product?
  5. Oct 17, 2005 #4
    Hi , I don't know what you mean but I guess you want to know that
    "a x b" means a cross product with b
    "a.b" mean a dot b
    Thank you
  6. Oct 17, 2005 #5


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    Right. So, is "dot" vector multiplication? How is "cross product" different than vector multiplication? Some examples would be useful. What is (1,2) x (3,4)? What is (1,2).(3,4)?
    Let's say a, b, and c are vectors. Let a=(1,2), b=(1,2) and c=(c1,c2).
    ab = ac ---> a1b1 + a2b2 = a1c1 + a2c2 ---> 5 = c1 + 2 c2 ---> c1 = 5 - 2 c2, which means that although c = (1,2) would satisfy the equation, so would c = (5,0). Therefore what you want to demonstrate is not demonstrable on the basis of vector multiplication alone. That is why more info is needed on the exact definitions of the cross and the dot.

    My guess is they are inner and outer products: a.b = a1b1 + a2b2, axb = (a1b1, a1b2, a2b1, a2b2). But can you verify this so we won't be making a mistake?
    Last edited: Oct 17, 2005
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