111 lines
2.4 KiB
Plaintext
111 lines
2.4 KiB
Plaintext
ans
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018494
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$\overrightarrow{MA}=-\dfrac{1}{2}\overrightarrow{a}-\dfrac{1}{2}\overrightarrow{b}$, $\overrightarrow{MB}=\dfrac{1}{2}\overrightarrow{a}-\dfrac{1}{2}\overrightarrow{b}$, $\overrightarrow{MC}=\dfrac{1}{2}\overrightarrow{a}+\dfrac{1}{2}\overrightarrow{b}$, $\overrightarrow{MD}=-\dfrac{1}{2}\overrightarrow{a}+\dfrac{1}{2}\overrightarrow{b}$
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023635
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证明略
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009628
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$\overrightarrow{OA}=a\cos \theta \overrightarrow{i}+a\sin\theta\overrightarrow{j}$, $\overrightarrow{OA'}=a\cos\theta\overrightarrow{i}-a\sin\theta\overrightarrow{j}$
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009629
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$\overrightarrow{OC}=-\overrightarrow{a}$, $\overrightarrow{OD}=-\overrightarrow{b}$, $\overrightarrow{DC}=-\overrightarrow{a}+\overrightarrow{b}$, $\overrightarrow{BC}=-\overrightarrow{a}-\overrightarrow{b}$
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009630
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$\overrightarrow{AG}=-\dfrac{1}{3}\overrightarrow{a}+\dfrac{2}{3}\overrightarrow{b}-\dfrac{1}{3}\overrightarrow{a}$, $\overrightarrow{BG}=\dfrac{2}{3}\overrightarrow{a}-\dfrac{1}{3}\overrightarrow{b}$, $\overrightarrow{CG}=-\dfrac{1}{3}\overrightarrow{a}-\dfrac{1}{3}\overrightarrow{b}$
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023636
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证明略
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018523
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D
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018524
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$(\dfrac{1}{2},\dfrac{3}{2})$
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018493
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$-5$, $-\dfrac{5}{2}$
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018497
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$m=-\dfrac{\sqrt{3}}{3}$, $n=-\dfrac{1}{3}$
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023637
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$[1,3]$
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018498
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$\overrightarrow{a}=\overrightarrow{b}=(1,2)$, $\overrightarrow{c}=(1,-2)$
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018499
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$(23,4)$
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018500
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$\overrightarrow{AC}=(-3,2)$, $\overrightarrow{BC}=(2,1)$
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018501
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$(\dfrac{4}{5},-\dfrac{3}{5})$
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018503
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$(4,6)$或$(2,2)$或$(-6,0)$
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018504
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B
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009631
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$3\overrightarrow{a}-\overrightarrow{b}=(-8,14)$, $|3\overrightarrow{a}-\overrightarrow{b}|=2\sqrt{65}$
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009632
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$(\dfrac{3}{5},-\dfrac{4}{5})$
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009633
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$\overrightarrow{AB}=(1,1)$, $\overrightarrow{BC}=(2,2)$, $\overrightarrow{AC}=(3,3)$, 共线证明略
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018509
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$\arccos\dfrac{\sqrt{2}}{10}$
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018506
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证明略
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018507
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证明略
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018508
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$\sqrt{10}$
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009634
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$\overrightarrow{a}\cdot\overrightarrow{b}=8$, $\overrightarrow{c}\cdot (\overrightarrow{a}-\overrightarrow{b})=-2$
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009635
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$|\overrightarrow{a}|=5$, $|\overrightarrow{b}|=13$, $\langle \overrightarrow{a},\overrightarrow{b} \rangle = \arccos\dfrac{33}{65}$
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009636
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$0$或$2$
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024787
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$0$或$-\dfrac{1}{2}$
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024778
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$2$千米
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024779
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$16-18\sqrt{3}$
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024781
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相反
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024782
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$-3$
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024783
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$-\dfrac{1}{m}\overrightarrow{a}$
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024784
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$\dfrac{2}{3}\overrightarrow{AB}+\dfrac{1}{3}\overrightarrow{AC}$
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024785
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$-\dfrac{1}{3}\overrightarrow{a}+\dfrac{2}{3}\overrightarrow{b}$
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024786
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$\dfrac{5}{13}$, $\dfrac{1}{13}$
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