Given: vectors $Z_{{?}_{?}}(1),Z_{{?}_{?}}(2)$ by way of their Cartesian coordinates $x_1,Y_1$ and $x_2,Y_2,$ determine the resultant $Z_{{?}_{?}}(R)=Z_{{?}_{?}}(1)+Z_{{?}_{?}}(2),$ by declaring its Cartesian coordinates $x_R,Y_R,$ and its magnitude $Z_R$ and direction ${}_R.$ Also report the positive magnitudes $Z_1,Z_2$ and associated directions ${}_{Z1},{}_{Z2}$ for $Z_{{?}_{?}}(1),Z_{{?}_{?}}(2).$ Use the dot product to report the $c_{12}=cos({}_{12})=cos({}_{21})$ and the result of $co{s}^{-1}(c_{12}).$ Choose the graph as usual. Finally, be sure to keep angles between $-180$ and $+180.$

First Example. Given $x_1=2\mathrm{.}12132lbf,Y_1=2\mathrm{.}12132lbf,x_2=0\mathrm{.}00000lbf,$ and $Y_2=3\mathrm{.}00000lbf,$ declare the unknown values.

$\backslash$table$[[x_R,2\mathrm{.}12,($lbf$)$