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Dot product, is (a.b).(a.b)=(a.a).(b.b) ?

  1. Dec 14, 2012 #1

    As I remember, dot product is commutative, and so (a.b).(a.b) = (a.a).(b.b)
    But when I apply to simple vectors it is all wrong, e.g:
    a = (2, 2, 0)
    b = (1, 0, 0)

    (a.b).(a.b) = 2.2 = 4
    (a.a).(b.b) = 8.1 = 8

    Why are they different? Pls explain for me

  2. jcsd
  3. Dec 14, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    That is not what "commutative" means. It meas that (a.b) = (b.a)

    It should be obvious that (a.b).(a.b) is not equal to (a.a).(b.b) in general. For example (a.b) can be 0 when (a.a) and (b.b) are both greater than 0.
  4. Dec 14, 2012 #3


    Staff: Mentor

    Also, your notation is misleading -- "(a.b).(a.b)". You are using a period (.) to indicate two different types of multiplication: the dot or scalar product that is defined for two vectors, and ordinary multiplication of real numbers.

    Slightly better notation would be (a.b)(a.b), with nothing shown for the real number multiplication.

    Even better would be to use a dot for the dot product, for which some simple LaTeX can be used: (a ##\cdot## b)(a ##\cdot## b).
  5. Dec 15, 2012 #4
    Many thanks
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