知识点挑题 - 高中数学 - 优优班--学霸训练营

2．如图所示，在平行六面体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)中，\(M\)为\(A_{1}C_{1}\)与\(B_{1}D_{1}\)的交点\(.\)若\(\overrightarrow{AB}=a\)，\(\overrightarrow{AD}=b\)，\(\overrightarrow{A{{A}_{1}}}=c\)，则下列向量中与\(\overrightarrow{BM}\)相等的向量是 \((\) \()\)

A．\(-\dfrac{1}{2}a+\dfrac{1}{2}b+c\)

B．\(\dfrac{1}{2}a+\dfrac{1}{2}b+c\)

C．\(-\dfrac{1}{2}a-\dfrac{1}{2}b+c\)

D．\(\dfrac{1}{2}a-\dfrac{1}{2}b+c\)

难度：易

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3．

正方体\(ABCD-{A}_{1}{B}_{1}{C}_{1}{D}_{1} \)的棱长为\(1\)，以\(D\)为原点，\( \overrightarrow{DA}, \overrightarrow{DC}, \overrightarrow{D{D}_{1}} \)所在直线为\(x\)，\(y\)，\(z\)轴建立直角坐标系\(D-xyz\)，且\(MN\)是\(A{B}_{1} \)与\(B{C}_{1} \)的公垂线，\(M\)在\(A{B}_{1} \)上，\(N\)在\(B{C}_{1} \)上，则\( \overrightarrow{MN}= (\)　　\()\)

A．\(\left(1,- \dfrac{2}{3}, \dfrac{2}{3}\right) \)

B．\(\left(- \dfrac{2}{3},1,- \dfrac{2}{3}\right) \)

C．\(\left(- \dfrac{1}{3}, \dfrac{1}{3},- \dfrac{1}{3}\right) \)

D．\(\left( \dfrac{1}{3},- \dfrac{1}{3},- \dfrac{2}{3}\right) \)

难度：易

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4．

在正方体中\(ABCD-A_{1}B_{1}C_{1}D_{1}\)，若\(G\)点是\(\triangle BA_{1}D\)的重心，且\( \overrightarrow{AG}=x \overrightarrow{AD}+y \overrightarrow{AB}+z \overrightarrow{CC_{1}}\)，则\(x+y+z\)的值为\((\)　　\()\)

A．\(3\)

B．\(1\)

C．\(-1\)

D．\(-3\)

难度：易

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5．
若向量\(\overset{\underrightarrow{}}{a}{=}(1{,}1{,}x){,}\overset{\underrightarrow{}}{b}{=}(1{,}2{,}1){,}\overset{\underrightarrow{}}{c}{=}(1{,}1{,}1)\)，满足条件\((\overset{\underrightarrow{}}{c}{-}\overset{\underrightarrow{}}{a}){·}(2\overset{\underrightarrow{}}{b}){=-}2\)，则\(x{=}\)__________．

难度：易

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