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This is what I have, is it enough to show this?

ab = (ax, ay, az) [tex]\dot[/tex] (bx, by, bz) = axbx + ayby + azbz;

a[tex]\dot[/tex]b = (axi + ayj) (bxi + byj); //note: i and j are unit vectors

= axbx(i)(i) + ayby(j)(j) + axby(i)(j) + aybx(j)(i)

= axbx+ayby

b[tex]\dot[/tex]a = (bx, by, bz) [tex]\dot[/tex] (ax,ay,az) = bxax + byay + bzaz;

b[tex]\dot[/tex]a = (bxi + byj) (axi + ayj)

= bxax(i)(i) + byay(j)(j) + bxay(i)(j) + byax(j)(i)

= bxax + byay

Is this enough to show the dot product is communative?

Any help would be great if it isn't!