Two vectors vec$(A)$ and vec$(B)$ are shown in the figure. Vector vec$(A)$ has a magnitude of $r_A=22\mathrm{.}5$ and an angle of ${}_A=32\mathrm{.}3.$ Vector vec$(B)$ has a magnitude of $r_B=42\mathrm{.}9$ and an angle of ${}_B=63\mathrm{.}9.$ The figure is not to scale.

Express each vector in the figure using ijk unit vector notation,

vec$(A)=A_{x}i+A_{y}j$

vec$(B)=B_{x}i+B_{y}j$

where $A_x,A_y,B_x,$ and $B_y$ are the calculated values of the $x$ and $y-$components of vectors vec$(A)$ and vec$(B),$ respectively.

vec$(A)=$

vec$(B)=$