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[几何] 一道梯形中的两平面向量积问题

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敬畏数学 posted 2018-5-1 16:44 |Read mode
梯形$ABCD,AB\px CD,AB=a,AD=b,CD=c(a\ne2c),\overrightarrow{AC}*\overrightarrow{BC}=m,$则$\overrightarrow{AD}*\overrightarrow{CD}=?$

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realnumber posted 2018-5-1 22:47
向量积$\vv{a}\times\vv{b}$
与数量积$\vv{a}·\vv{b}$意义不一样.可问度姑娘

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realnumber posted 2018-5-1 22:55
数量积可这样解
设$\vv{AD}=\vv{x},\vv{DC}=\vv{y},\vv{AB}=\frac{a}{c}\vv{y},\vv{AC}=\vv{x}+\vv{y},$后面你自己算吧

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走走看看 posted 2022-3-4 11:12
Last edited by 走走看看 2022-3-4 11:19回复 1# 敬畏数学

向量题4.png

$\vv{AC}=\vv{b}+\vv{c},\vv{BC}=\vv{a}+\vv{b}+\vv{c}$

$\vv{a}=-\frac{a}{c}\vv{c}$

$m=\vv{AC}\vv{BC}=(\vv{b}+\vv{c})(-\frac{a}{c}\vv{c}+\vv{b}+\vv{c})$

展开可得 :

$-\vv{b}\vv{c}=\frac{c(m-b^2-c^2+ac)}{a-2c}$

另外,向量点积的符号,在拼音输入时,可用“dian”选择输入。

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isee posted 2022-3-4 11:59
回复 4# 走走看看

数学中的 点积,代码 \cdot ,这是一个点 \cdots ,连续三个点
\dot a ,是a 上方一点

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