2024年陕西省初中学业水平考试仿真卷(六)6数学.考卷答案

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2024年陕西省初中学业水平考试仿真卷(六)6数学.考卷答案试卷答案

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分析(1)由已知得BM$\underset{∥}{=}$NC′,从而BMC′N是平行四边形,能求出能化简$\overrightarrow{AM}$+$\overrightarrow{BN}$.
(2)结合三棱柱,利用向量加法法则能化简$\overrightarrow{A′N}$-$\overrightarrow{MC′}$+$\overrightarrow{BB′}$.

解答解:(1)∵在三棱柱ABC-A′B′C′中,M,N分别内BC,B′C′的中点,
∴BM$\underset{∥}{=}$NC′,∴BMC′N是平行四边形,
∴$\overrightarrow{AM}$+$\overrightarrow{BN}$=$\overrightarrow{AM}+\overrightarrow{M{C}^{'}}$=$\overrightarrow{A{C}^{'}}$.
(2)$\overrightarrow{A′N}$-$\overrightarrow{MC′}$+$\overrightarrow{BB′}$
=$\overrightarrow{AM}$+$\overrightarrow{B{B}^{'}}$+$\overrightarrow{{C}^{'}M}$
=$\overrightarrow{AM}$+$\overrightarrow{C{C}^{'}}$+$\overrightarrow{{C}^{'}M}$
=$\overrightarrow{AM}$+$\overrightarrow{CM}$
=$\overrightarrow{AM}$+$\overrightarrow{MB}$
=$\overrightarrow{AB}$.

点评本题考查向量的化简,是基础题,解题时要认真审题,注意数形结合思想的合理运用.