From 71ac9ca5f85c49428adee3cbbe621f5147635e72 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Tue, 23 Apr 2024 12:30:24 +0800 Subject: [PATCH] =?UTF-8?q?=E5=AF=BC=E5=85=A5=E4=B8=80=E4=BA=9B=E9=AB=98?= =?UTF-8?q?=E4=B8=80=E7=9A=84=E7=AD=94=E6=A1=88?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v3/文本文件/metadata.txt | 648 +++++------------------------------ 1 file changed, 78 insertions(+), 570 deletions(-) diff --git a/工具v3/文本文件/metadata.txt b/工具v3/文本文件/metadata.txt index d9f9b2e0..fd1ad96a 100644 --- a/工具v3/文本文件/metadata.txt +++ b/工具v3/文本文件/metadata.txt @@ -1,608 +1,116 @@ -usages +ans +018470 +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): $\overrightarrow{BD}$, $\overrightarrow{DC}$ -024403 -20240419 2024届高三11班 1.000 +018471 +$\overrightarrow{EA}$, $\overrightarrow{BE}$, $\overrightarrow{DF}$ +023627 +证明略 -024404 -20240419 2024届高三11班 1.000 +018476 +合力为$10\mathrm{N}$, 合力与铅垂方向偏离约$36.87^\circ$ +018477 +$\sqrt{3}$ -024405 -20240419 2024届高三11班 1.000 +018478 +直角三角形($A=90^\circ$) +009615 +(1) $\overrightarrow{EF}$, $\overrightarrow{CB}$, $\overrightarrow{DO}$;\\ +(2) $\overrightarrow{BO}$, $\overrightarrow{OE}$, $\overrightarrow{EO}$, $\overrightarrow{AF}$, $\overrightarrow{FA}$, $\overrightarrow{BE}$, $\overrightarrow{EB}$, $\overrightarrow{CD}$, $\overrightarrow{DC}$;\\ +(3) $\overrightarrow{AB}$, $\overrightarrow{BA}$, $\overrightarrow{BC}$, $\overrightarrow{CB}$, $\overrightarrow{CD}$, $\overrightarrow{DC}$, $\overrightarrow{DE}$, $\overrightarrow{ED}$, $\overrightarrow{EF}$, $\overrightarrow{FE}$, $\overrightarrow{FA}$, $\overrightarrow{AF}$, $\overrightarrow{OA}$, $\overrightarrow{AO}$, $\overrightarrow{OB}$, $\overrightarrow{BO}$, $\overrightarrow{CO}$, $\overrightarrow{OD}$, $\overrightarrow{DO}$, $\overrightarrow{OE}$, $\overrightarrow{EO}$, $\overrightarrow{OF}$, $\overrightarrow{FO}$;\\ +(4) $\overrightarrow{BO}$, $\overrightarrow{OE}$, $\overrightarrow{AF}$, $\overrightarrow{CD}$ -024406 -20240419 2024届高三11班 0.929 +009616 +(1) $\overrightarrow{CB}$; (2) $\overrightarrow{BA}$ +009618 +不一定, 比如三向量平行的时候 -024407 -20240419 2024届高三11班 0.857 +018480 +(1) $-\overrightarrow{a}$; (2) $5\overrightarrow{a}+\overrightarrow{b}$; (3) $2\lambda\overrightarrow{b}-2\mu\overrightarrow{a}$ +018481 +$3\overrightarrow{a}-4\overrightarrow{b}$ -024408 -20240419 2024届高三11班 0.964 +018482 +(1) $2\overrightarrow{BC}-\dfrac{1}{2}\overrightarrow{BA}$; (2) $-\dfrac{3}{2}\overrightarrow{CB}-\dfrac{1}{2}\overrightarrow{CA}$ +018483 +$A,B,C$共线, 证明略 -024409 -20240419 2024届高三11班 1.000 +018484 +$\lambda=\dfrac{4}{9}$, $\mu=-\dfrac{7}{9}$ +009619 +(1) $17\overrightarrow{a}-10\overrightarrow{b}$; (2) $-\dfrac{7}{12}\overrightarrow{a}+\dfrac{13}{12}\overrightarrow{b}$; (3) $-11\overrightarrow{b}+11\overrightarrow{c}$ -031072 -20240419 2024届高三11班 0.857 +009621 +$\overrightarrow{AD}=-\dfrac{1}{2}\overrightarrow{a}+\overrightarrow{b}$; $\overrightarrow{AG}=-\dfrac{1}{3}\overrightarrow{a}+\dfrac{2}{3}\overrightarrow{b}$; $\overrightarrow{GC}=\dfrac{1}{3}\overrightarrow{a}+\dfrac{1}{3}\overrightarrow{b}$ +018486 +(1) 投影为$-\dfrac{2}{3}\overrightarrow{d}$, 数量投影为$-2$; (2) $-6$ -024410 -20240419 2024届高三11班 0.929 +018487 +证明略 +023633 +$\overrightarrow{AB}\cdot \overrightarrow{AC}=18$, $\overrightarrow{AB}\cdot\overrightarrow{BC}=-18$ -024411 -20240419 2024届高三11班 1.000 +018488 +$-\dfrac{3}{2}$ +009622 +证明略 -024403 -20240419 2024届高三04班 0.963 +009623 +(1) $\dfrac{\pi}{3}$; (2) $\dfrac{\pi}{3}$; (3) $\dfrac{2\pi}{3}$ +009624 +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$-\dfrac{24}{5}$ -024404 -20240419 2024届高三04班 1.000 +023631 +$-\dfrac{1}{8}\overrightarrow{a}$ +023629 +$\sqrt{3}$或$\sqrt{7}$ -024405 -20240419 2024届高三04班 0.963 +023630 +$\dfrac{9}{4}$ +023628 +\textcircled{2} -024406 -20240419 2024届高三04班 1.000 +023632 +证明略 +018490 +证明略 -024407 -20240419 2024届高三04班 0.667 +018491 +$6$ +018489 +证明略 -024408 -20240419 2024届高三04班 1.000 +018492 +$10$ +004258 +$1$或$\dfrac{1}{4}$ -024409 -20240419 2024届高三04班 0.889 +009626 +(1) $16-18\sqrt{3}$; (2) $\dfrac{2\pi}{3}$ +009627 +$\sqrt{7}$ -031072 -20240419 2024届高三04班 1.000 +010349 +$-16$ - 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