1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Show the commutative property with dot product

  1. Sep 9, 2005 #1
    Hello everyone, does anyone know the proof of the dot products communative property (a)(b) = (b)(a) or any websites that show the dot products communative property? or other properties? Thanks! The book only shows the distributed property.
     
  2. jcsd
  3. Sep 9, 2005 #2

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Write a.b and then b.a in terms of the components or as |a||b|cosO. Commutativity of the dot products follows from commutativity of addition (resp. multiplication) in [itex]\mathbb{R}[/itex].
     
  4. Sep 9, 2005 #3

    Astronuc

    User Avatar

    Staff: Mentor

    (a1 i + b1 j) [itex]\bullet[/itex] (a2 i + b2 j) =

    a1 i [itex]\bullet[/itex] a2 i + a1 i [itex]\bullet[/itex] b2 j + b1 j [itex]\bullet[/itex] a2 i + b1 j [itex]\bullet[/itex] b2 j =

    remember i [itex]\bullet[/itex] i = j [itex]\bullet[/itex] j = 1, and i [itex]\bullet[/itex] j = j [itex]\bullet[/itex] i = 0,

    then regroup and show something similar to

    a * b = b * a

    and this can be extended to 3 dimensions
     
  5. Sep 9, 2005 #4
    well, the dot product is a definition.

    as such

    [tex]
    \vec{a}\bullet\vec{b}=

    \left(
    \begin{array}{cc}
    a_x \\
    a_y\\
    a_z
    \end{array}
    \right)
    \bullet
    \left(
    \begin{array}{cc}
    b_x \\
    b_y\\
    b_z
    \end{array}
    \right)
    =a_xb_x + a_yb_x + a_zb_z
    [/tex]

    so, what is [tex]\vec{b}\bullet\vec{a}[/tex]?
     
  6. Sep 10, 2005 #5
    Cool so all I really need to show is this? or doesn't this prove it yet? Thanks for the replies everyone
    [tex]
    \vec{b}\bullet\vec{a}=

    \left(
    \begin{array}{cc}
    b_x \\
    b_y\\
    b_z
    \end{array}
    \right)
    \left(
    \begin{array}{cc}
    a_x \\
    a_y\\
    a_z
    \end{array}
    \right)
    \bullet

    =b_xa_x + b_xa_y + b_za_z
    [/tex]
     
  7. Sep 10, 2005 #6

    Doc Al

    User Avatar

    Staff: Mentor

    You need to show that
    [tex]\vec{b}\bullet\vec{a} = \vec{a}\bullet\vec{b}[/tex]

    Evaluate each side and compare. Make use of the commutivity of ordinary addition, as quasar987 advised.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Show the commutative property with dot product
  1. Dot product (Replies: 4)

Loading...