${\text{I}}^2+{\text{II}}^2+{\text{III}}^2$

Prediction

Experiment

$A^2\left(p^{+}\right)=\overrightarrow{A}\left(p^{+}\right)\cdot \overrightarrow{A}\left(p^{+}\right)$

${\text{I}}^2\propto {\left(+2\right)}^2+{\left(-13\right)}^2+{\left(+11\right)}^2=294$

774

$\mathrm{<mo>\; |\; </mo>\; <mo>\; |\; </mo>\; <mo>\; |\; </mo>}$

$\iff$

${\text{II}}^2\propto {\left(-16\right)}^2+{\left(+5\right)}^2+{\left(+11\right)}^2=402$

$774+1098=1872$

$938+940=1878$

${\text{III}}^2\propto {\left(+2\right)}^2+{\left(+5\right)}^2+{\left(-7\right)}^2=78$

$1872/2=936$

$1878/2=939$

$A^2\left(n^0\right)=\overrightarrow{A}\left(n^0\right)\cdot \overrightarrow{A}\left(n^0\right)$

${\text{I}}^2\propto {\left(+2\right)}^2+{\left(-13\right)}^2+{\left(-7\right)}^2=222$

1098

$\mathrm{<mo>\; |\; </mo>\; <mo>\; |\; </mo>\; <mo>\; |\; </mo>}$

$774/936=0.827$

$\iff$

$938/939=0.999$

${\text{II}}^2\propto {\left(-16\right)}^2+{\left(-13\right)}^2+{\left(+11\right)}^2=546$

$1098/936=1.173$

$940/939=1.001$

${\text{III}}^2\propto {\left(-16\right)}^2+{\left(+5\right)}^2+{\left(-7\right)}^2=330$

$0.827+1.173=2$

$0.999+1.001=2$