117 lines
3.4 KiB
Plaintext
117 lines
3.4 KiB
Plaintext
ans
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018470
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与$\overrightarrow{EF}$平行的非零向量(除$\overrightarrow{EF}$外): $\overrightarrow{FE}$, $\overrightarrow{BD}$, $\overrightarrow{DB}$, $\overrightarrow{CD}$, $\overrightarrow{DC}$, $\overrightarrow{BC}$, $\overrightarrow{CB}$; 与$\overrightarrow{EF}$相等的向量(除$\overrightarrow{EF}$外): $\overrightarrow{BD}$, $\overrightarrow{DC}$
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018471
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$\overrightarrow{EA}$, $\overrightarrow{BE}$, $\overrightarrow{DF}$
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023627
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证明略
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018476
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合力为$10\mathrm{N}$, 合力与铅垂方向偏离约$36.87^\circ$
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018477
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$\sqrt{3}$
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018478
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直角三角形($A=90^\circ$)
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009615
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(1) $\overrightarrow{EF}$, $\overrightarrow{CB}$, $\overrightarrow{DO}$;\\
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(2) $\overrightarrow{BO}$, $\overrightarrow{OE}$, $\overrightarrow{EO}$, $\overrightarrow{AF}$, $\overrightarrow{FA}$, $\overrightarrow{BE}$, $\overrightarrow{EB}$, $\overrightarrow{CD}$, $\overrightarrow{DC}$;\\
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(3) $\overrightarrow{AB}$, $\overrightarrow{BA}$, $\overrightarrow{BC}$, $\overrightarrow{CB}$, $\overrightarrow{CD}$, $\overrightarrow{DC}$, $\overrightarrow{DE}$, $\overrightarrow{ED}$, $\overrightarrow{EF}$, $\overrightarrow{FE}$, $\overrightarrow{FA}$, $\overrightarrow{AF}$, $\overrightarrow{OA}$, $\overrightarrow{AO}$, $\overrightarrow{OB}$, $\overrightarrow{BO}$, $\overrightarrow{CO}$, $\overrightarrow{OD}$, $\overrightarrow{DO}$, $\overrightarrow{OE}$, $\overrightarrow{EO}$, $\overrightarrow{OF}$, $\overrightarrow{FO}$;\\
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(4) $\overrightarrow{BO}$, $\overrightarrow{OE}$, $\overrightarrow{AF}$, $\overrightarrow{CD}$
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009616
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(1) $\overrightarrow{CB}$; (2) $\overrightarrow{BA}$
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009618
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不一定, 比如三向量平行的时候
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018480
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(1) $-\overrightarrow{a}$; (2) $5\overrightarrow{a}+\overrightarrow{b}$; (3) $2\lambda\overrightarrow{b}-2\mu\overrightarrow{a}$
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018481
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$3\overrightarrow{a}-4\overrightarrow{b}$
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018482
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(1) $2\overrightarrow{BC}-\dfrac{1}{2}\overrightarrow{BA}$; (2) $-\dfrac{3}{2}\overrightarrow{CB}-\dfrac{1}{2}\overrightarrow{CA}$
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018483
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$A,B,C$共线, 证明略
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018484
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$\lambda=\dfrac{4}{9}$, $\mu=-\dfrac{7}{9}$
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009619
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(1) $17\overrightarrow{a}-10\overrightarrow{b}$; (2) $-\dfrac{7}{12}\overrightarrow{a}+\dfrac{13}{12}\overrightarrow{b}$; (3) $-11\overrightarrow{b}+11\overrightarrow{c}$
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009621
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$\overrightarrow{AD}=-\dfrac{1}{2}\overrightarrow{a}+\overrightarrow{b}$; $\overrightarrow{AG}=-\dfrac{1}{3}\overrightarrow{a}+\dfrac{2}{3}\overrightarrow{b}$; $\overrightarrow{GC}=\dfrac{1}{3}\overrightarrow{a}+\dfrac{1}{3}\overrightarrow{b}$
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018486
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(1) 投影为$-\dfrac{2}{3}\overrightarrow{d}$, 数量投影为$-2$; (2) $-6$
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018487
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证明略
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023633
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$\overrightarrow{AB}\cdot \overrightarrow{AC}=18$, $\overrightarrow{AB}\cdot\overrightarrow{BC}=-18$
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018488
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$-\dfrac{3}{2}$
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009622
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证明略
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009623
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(1) $\dfrac{\pi}{3}$; (2) $\dfrac{\pi}{3}$; (3) $\dfrac{2\pi}{3}$
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009624
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当$\cos\langle \overrightarrow{a},\overrightarrow{b}\rangle = 0.8$时, 投影为$\dfrac{24}{25}\overrightarrow{a}$, 数量投影为$\dfrac{24}{5}$; 当$\cos\langle \overrightarrow{a},\overrightarrow{b}\rangle = -0.8$时, 投影为$-\dfrac{24}{25}\overrightarrow{a}$, 数量投影为$-\dfrac{24}{5}$
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023631
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$-\dfrac{1}{8}\overrightarrow{a}$
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023629
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$\sqrt{3}$或$\sqrt{7}$
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023630
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$\dfrac{9}{4}$
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023628
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\textcircled{2}
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023632
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证明略
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018490
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证明略
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018491
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$6$
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018489
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证明略
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018492
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$10$
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004258
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$1$或$\dfrac{1}{4}$
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009626
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(1) $16-18\sqrt{3}$; (2) $\dfrac{2\pi}{3}$
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009627
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$\sqrt{7}$
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010349
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$-16$
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023634
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$3$
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