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Scalar product to prove triangle inequality?

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data
    From the inequality

    |a.b| <= |a||b|

    prove the triangle inequality:

    |a+b| <= |a| + |b|


    2. Relevant equations

    a.b = |a|b| cos theta



    3. The attempt at a solution

    Making a triangle where side c = a+b. Don't know how to approach the question.

    Thanks.
     
  2. jcsd
  3. Oct 7, 2012 #2
    I may not be understanding your question, but it seems like you should start with the Pythagorean Identities.
     
  4. Oct 7, 2012 #3
    Also think about what values your trig function is between
     
  5. Oct 7, 2012 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You should start by knowing |a+b|^2=(a+b).(a+b). Now expand the right side.
     
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