If $\overrightarrow{\mathrm{A}}$ = 4N, $\overrightarrow{\mathrm{B}}$ = 3N the value of ${\left|\overrightarrow{\mathrm{A}} \mathrm{x} \overrightarrow{\mathrm{B}}\right|}^2={\left|\overrightarrow{\mathrm{A}}.\overrightarrow{\mathrm{B}}\right|}^2$ then

A = 4N, B = 3N

${\left|\overline{\mathrm{A}} \mathrm{x} \overline{\mathrm{B}}\right|}^2+{\left|\overline{\mathrm{A}}.\overline{\mathrm{B}}\right|}^2={\mathrm{A}}^2{\mathrm{B}}^2\mathrm{sin\theta }+{\mathrm{A}}^2{\mathrm{B}}^2{\cos }^2\mathrm{\theta }$

$={\mathrm{A}}^2{\mathrm{B}}^2({\sin }^2\mathrm{\theta }+{\cos }^2\mathrm{\theta })={\mathrm{A}}^2{\mathrm{B}}^2={\left(4\right)}^2{\left(3\right)}^2$

= 16 x 9 = 144N