- #1

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- Thread starter mr_coffee
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- #1

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- #2

quasar987

Science Advisor

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- #3

Astronuc

Staff Emeritus

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a

remember

then regroup and show something similar to

a * b = b * a

and this can be extended to 3 dimensions

- #4

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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]?

- #5

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[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]

- #6

Doc Al

Mentor

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[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.

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