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Homework Help: Dot product proof

  1. Apr 27, 2010 #1
    If X is an N vector, is it 1) possible for X*X to be negative? 2) if x*x=0, what is X.

    I am having trouble writing the proper proof. for 1 I stated that it is impossible for X*X to be negative bc if x is positive, X*X is positive and if x is negative, -X*-X is still positive.

    for 2 I stated the properties of multiplication; in order for a product to = 0 one of the components must be 0.

    Can someone advise on the proper method for writing these proofs?

    Thanks
     
  2. jcsd
  3. Apr 27, 2010 #2

    Dick

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    What is X.X in terms of the components of X?
     
  4. Apr 28, 2010 #3
    Not sure what youare asking, but X*X is the dot product of X. X is an arbitrary vector.
     
  5. Apr 28, 2010 #4

    Dick

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    X is a vector, it has components. I.e. X=(x1,x2,...,xn). What's X.X in terms of the components, the little x's?
     
  6. Apr 28, 2010 #5

    lanedance

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    I think Dick is asking you to examine how the dot product is caclulated in terms of the components of the vector.

    Say X = (x1, x2, .. ,xn)^T

    How do you calculate the dot product X*X in terms of the xi's?
     
  7. Apr 28, 2010 #6
    X= ( X1, X2, X3)
    the dot product should be X1^2+X2^2 +X3^2. Squares cant be negative.


    if X1^2+X2^2 +X3^2 =0 then X1 X2 and X3 must be zero

    Is this all there is to it?
     
  8. Apr 28, 2010 #7

    lanedance

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    looks good to me
     
  9. Apr 28, 2010 #8

    lanedance

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    though you should generalise it to the n dimensional case rather than just 3
     
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