71. You are to program a robotic arm on an assembly line to move in the $x y$-plane. Its first displacement is $\vec{A}$; its second displacement is $\overrightarrow{\boldsymbol{B}}$, of magnitude $6.40 \mathrm{~cm}$ and direction $63.0^{\circ}$ measured in the sense from the $+x$-axis toward the $-y$-axis.

 71. You are to program a robotic arm on an assembly line to move in the $x y$-plane. Its first displacement is $\vec{A}$; its second displacement is $\overrightarrow{\boldsymbol{B}}$, of magnitude $6.40 \mathrm{~cm}$ and direction $63.0^{\circ}$ measured in the sense from the $+x$-axis toward the $-y$-axis. The resultant $\vec{C}=\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}$ of the two displacements should also have a magnitude of $6.40 \mathrm{~cm}$, but a direction $22.0^{\circ}$ measured in the sense from the $+x-a x$ is toward the $+y$-axis. (a) Draw the vector addition diagram for these vectors, roughly to scale. (b) Find the components of $\vec{A}$. (c) Find the magnitude and direction of $\vec{A}$