[tex]\displaystyle\\
A(5,~-2)~~\Longrightarrow~~\overset{\rightarrow}{a}=5i-2j\\\\
C(1,~2)~~\Longrightarrow~~\overset{\rightarrow}{c}=i+2j\\\\
\overset{\rightarrow}{b}=\overset{\rightarrow}{a}+\overset{\rightarrow}{c}=
(5i-2j) + (i+2j) = \boxed{\bf 6i+0j}\\\\
\Longrightarrow~~B(6,~0)[/tex]