Cho hình hộp ABCD.A'B'C'D', đặt \(\overrightarrow{AB}=\overrightarrow{a},\overrightarrow{AD}=\overrightarrow{b},\overrightarrow{AA'}=\overrightarrow{c},\) thì đẳng thức nào sau đây đúng?
A. \(\overrightarrow{BD'}=-\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\)
B. \(\overrightarrow{BD'}=\overrightarrow{a}-\overrightarrow{b}-\overrightarrow{c}\)
C. \(\overrightarrow{BD'}=\overrightarrow{a}+\overrightarrow{b}-\overrightarrow{c}\)
D. \(\overrightarrow{BD'}=\overrightarrow{a}-\overrightarrow{b}+\overrightarrow{c}\)
\(\overrightarrow{BD'}=\overrightarrow{BA}+\overrightarrow{AD}+\overrightarrow{DD'}=-\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{AA'}\)
\(=-\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\)