《2025年教材帮高中数学选择性必修第二册苏教版》

例2-2[多选题] (2025·河北省承德市期中) 在平行六面体$ABCD - A_1B_1C_1D_1$中，下列各式中运算的结果为向量$\overrightarrow{BD_1}$的是（）
A.$(\overrightarrow{BC} + \overrightarrow{BB_1}) - \overrightarrow{D_1C_1}$
B.$(\overrightarrow{A_1D_1} - \overrightarrow{A_1A}) - \overrightarrow{AB}$
C.$(\overrightarrow{AD} - \overrightarrow{AB}) + \overrightarrow{DD_1}$
D.$(\overrightarrow{B_1D_1} - \overrightarrow{A_1A}) - \overrightarrow{DD_1}$

答案： 解析 A中，$(\overrightarrow{BC} + \overrightarrow{BB_1}) - \overrightarrow{D_1C_1} = \overrightarrow{BC_1} - \overrightarrow{D_1C_1} = \overrightarrow{BC_1} + \overrightarrow{C_1D_1} = \overrightarrow{BD_1}$;
B中，$(\overrightarrow{A_1D_1} - \overrightarrow{A_1A}) - \overrightarrow{AB} = \overrightarrow{AD_1} - \overrightarrow{AB} = \overrightarrow{BD_1}$;
C中，$(\overrightarrow{AD} - \overrightarrow{AB}) + \overrightarrow{DD_1} = \overrightarrow{BD} + \overrightarrow{DD_1} = \overrightarrow{BD_1}$;
D中，$(\overrightarrow{B_1D_1} - \overrightarrow{A_1A}) - \overrightarrow{DD_1} = (\overrightarrow{B_1D_1} - \overrightarrow{B_1B}) - \overrightarrow{DD_1} = \overrightarrow{BD_1} + \overrightarrow{D_1D} = \overrightarrow{BD}$.
故选ABC.
答案 ABC