知识点挑题 - 高中数学 - 优优班--学霸训练营

设\(x\)，\(y∈R\)，向量\( \overset{→}{a}=\left(x,1,0\right), \overset{→}{b}=\left(1,y,0\right), \overset{→}{c}=\left(2,-4,0\right) \)且\(\overrightarrow{a}\bot \overrightarrow{c},\overrightarrow{b}/\!/\overrightarrow{c},\)，则\(|\overrightarrow{a}+\overrightarrow{b}|=(\) \()\)　

A．\(\sqrt{5}\)　

B．\(\sqrt{10}\)

C．\(2\sqrt{5}\)　

D．\(10\)

难度：较易

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2．

已知\(a=(1-t,2t-1,0)\)，\(b=(2,t,t)\)，则\(|b-a|\)的最小值

A．\(\sqrt{5}\)

B．\(\sqrt{6}\)

C．\(\sqrt{2}\)

D．\(\sqrt{3}\)

难度：较易

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3．

在平行六面体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)中，\(AC\)与\(BD\)的交点为\(M\)，设\( \overrightarrow{{A}_{1}{B}_{1}}= \overrightarrow{a}, \overrightarrow{{A}_{1}{D}_{1}}= \overrightarrow{b}, \overrightarrow{{A}_{1}A=c} \)，则\( \overrightarrow{{D}_{1}M}= =(\)　　\()\)

A．\(- \dfrac{1}{2} \overrightarrow{a}+ \dfrac{1}{2} \overrightarrow{b}+ \overrightarrow{c} \)

B．\( \dfrac{1}{2} \overrightarrow{a}- \dfrac{1}{2} \overrightarrow{b}+ \overrightarrow{c} \)

C．\( \dfrac{1}{2} \overrightarrow{a}+ \dfrac{1}{2} \overrightarrow{b}+ \overrightarrow{c} \)

D．\(- \dfrac{1}{2} \overrightarrow{a}- \dfrac{1}{2} \overrightarrow{b}+ \overrightarrow{c} \)

难度：较易

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4．

如图，在三棱柱\(ABC-A_{1}B_{1}C_{1}\)中，\(M\)为\(A_{1}C_{1}\)的中点，若\( \overrightarrow{AB}=a,AA1= \overrightarrow{c}, \overrightarrow{BC}= \overrightarrow{b} \)，则\( \overrightarrow{BM} \)可表示为\((\)　　\()\)

A．\(- \dfrac{1}{2} \overrightarrow{a}+ \dfrac{1}{2} \overrightarrow{b}+ \overrightarrow{c} \)

B．\( \dfrac{1}{2} \overrightarrow{a}+ \dfrac{1}{2} \overrightarrow{b}+ \overrightarrow{c} \)

C．\(- \dfrac{1}{2} \overrightarrow{a}- \dfrac{1}{2} \overrightarrow{b}+ \overrightarrow{c} \)

D．\( \dfrac{1}{2} \overrightarrow{a}- \dfrac{1}{2} \overrightarrow{b}+ \overrightarrow{c} \)

难度：较易

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5．

如图，在三棱柱\(ABC-A_{1}B_{1}C_{1}\)中，\(M\)为\(A_{1}C_{1}\)的中点，若\( \overrightarrow{AB}= \overrightarrow{a}\)，\( \overrightarrow{AA_{1}}= \overrightarrow{c}\)，\( \overrightarrow{BC}= \overrightarrow{b}\)，则\( \overrightarrow{BM}\)可表示为\((\)　　\()\)

A．\(- \dfrac {1}{2} \overrightarrow{a}+ \dfrac {1}{2} \overrightarrow{b}+ \overrightarrow{c}\)

B．\( \dfrac {1}{2} \overrightarrow{a}+ \dfrac {1}{2} \overrightarrow{b}+ \overrightarrow{c}\)

C．\(- \dfrac {1}{2} \overrightarrow{a}- \dfrac {1}{2} \overrightarrow{b}+ \overrightarrow{c}\)

D．\( \dfrac {1}{2} \overrightarrow{a}- \dfrac {1}{2} \overrightarrow{b}+ \overrightarrow{c}\)

难度：较易

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