Find the domain of the vector function $\displaystyle \vec{{r}}{\left({t}\right)}=<\sqrt{{{t}+{2}}},\frac{{1}}{\sqrt{{{t}+{2}}}},{\log{{\left({11}-{t}\right)}}}>$

Domain: $\displaystyle {\left\lbrace{t}{\mid}\right.}$ $\displaystyle <{t}<$ $\displaystyle {\rbrace}$