Trong không gian với hệ tọa độ Oxyz, cho hai vectơ khác $\overrightarrow{0}$, $\overrightarrow{a}\left( {{a}_{1}};{{a}_{2}};{{a}_{3}} \right),\overrightarrow{b}\left( {{b}_{1}};{{b}_{2}};{{b}_{3}} \right),$ khi đó $m\,\overrightarrow{a}+n\overrightarrow{b}$ bằng : $\left( m,n\in \mathbb{R} \right)$
A.$\left( m+n \right)\left( {{a}_{1}};{{a}_{2}};{{a}_{3}} \right)+\left( m+n \right)\left( {{b}_{1}};{{b}_{2}};{{b}_{3}} \right)$
B.$mn\left( {{a}_{1}}+{{b}_{1}};{{a}_{2}}+{{b}_{2}};{{a}_{3}}+{{b}_{3}} \right)$
C.$\left( m+n \right)\left( {{a}_{1}}+{{b}_{1}};{{a}_{2}}+{{b}_{2}};{{a}_{3}}+{{b}_{3}} \right)$
D.$\left( m{{a}_{1}}+n{{b}_{1}};m{{a}_{2}}+n{{b}_{2}};m{{a}_{3}}+n{{b}_{3}} \right)$