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Prove that the absolute value of a dot product is less than or equal t

  1. Jan 18, 2014 #1
    1. The problem statement, all variables and given/known data

    That is prove that |a•c|≤|a||c| for any vector a=<a1,a2,a3> & c=<c1,c2,c3>


    2. Relevant equations



    3. The attempt at a solution

    I really dont have much of an attempt at the solution. Im not sure where to start. I can kind of justify it in my mind by saying the sum of two magnitudes will always be a positive number and if 1 of the the a1 c1 etc where negative it could bring the value down but that is no where near a proof.

    Where does one even begin to start justifying this?
     
  2. jcsd
  3. Jan 19, 2014 #2

    Ibix

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    Science Advisor

    As always, start out by writing down everything relevant that you know. What is |a•c|? What are |a| and |c|? If you write them out, you will have some algebra to manipulate.
     
  4. Jan 19, 2014 #3
    lbix asked a perfectly reasonable question. Do you know an expression for the magnitude of the dot product of two vectors? Do you know, for example, what the dot product between two vectors signifies geometrically?
     
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