Cho hình hộp $ABCD.{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}$ . Khi đó: tổng 3 góc $(\overrightarrow{{{D}_{1}}{{A}_{1}}},\overrightarrow{C{{C}_{1}}})+(\overrightarrow{{{C}_{1}}B},\overrightarrow{D{{D}_{1}}})+(\overrightarrow{D{{C}_{1}}},\overrightarrow{{{A}_{1}}B})$là:

Cho hình hộp $ABCD.{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}$ . Khi đó: tổng 3 góc $(\overrightarrow{{{D}_{1}}{{A}_{1}}},\overrightarrow{C{{C}_{1}}})+(\overrightarrow{{{C}_{1}}B},\overrightarrow{D{{D}_{1}}})+(\overrightarrow{D{{C}_{1}}},\overrightarrow{{{A}_{1}}B})$là:

C. 1800

B. 2900

C.3600

D. 3150

Hướng dẫn

Ta có:

$\begin{align}

& (\overrightarrow{{{D}_{1}}{{A}_{1}}},\overrightarrow{C{{C}_{1}}})={{90}^{0}} \\

& (\overrightarrow{{{C}_{1}}B},\overrightarrow{D{{D}_{1}}})=(\overrightarrow{{{C}_{1}}B},\overrightarrow{C{{C}_{1}}})={{135}^{0}} \\

& (\overrightarrow{D{{C}_{1}}},\overrightarrow{{{A}_{1}}B})=(\overrightarrow{D{{C}_{1}}},\overrightarrow{{{D}_{1}}C})={{90}^{0}} \\

\end{align}$

$\Rightarrow (\overrightarrow{{{D}_{1}}{{A}_{1}}},\overrightarrow{C{{C}_{1}}})+(\overrightarrow{{{C}_{1}}B},\overrightarrow{D{{D}_{1}}})+(\overrightarrow{D{{C}_{1}}},\overrightarrow{{{A}_{1}}B})={{90}^{0}}+{{135}^{0}}+{{90}^{0}}={{315}^{0}}$

Chọn D