\(\vec{a}=2\overset{^}{i}-\overset{^}{j}+3\overset{^}{k},\overset{⇀}{b}=3\overset{^}{i}-5\overset{^}{j}+\overset{^}{k}If…

\(\vec{a}=2\overset{^}{i}-\overset{^}{j}+3\overset{^}{k},\overset{⇀}{b}=3\overset{^}{i}-5\overset{^}{j}+\overset{^}{k}If\vec{a}\times \vec{c}=\vec{c}\times \vec{b}\\ and(\vec{a}+\vec{c}).(\vec{c}+\vec{b})=168.then|\vec{c}{|}^{2}=________\)