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群里一道向量题目

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longzaifei Post time 2015-3-8 21:44 |Read mode
已知向量$a,b$满足$|a|=5,|b|\le 1$,且 $|a-4b|\le \sqrt{21} $,求$a.b $的最小值

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kuing Post time 2015-3-8 22:09
往下面看几个贴子就会看到了,kuing.cjhb.site/forum.php?mod=viewthread&tid=3346

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其妙 Post time 2015-3-9 12:12
\[\overrightarrow a  \cdot (\overrightarrow a  - 4\overrightarrow b ) \leqslant |\overrightarrow a | \cdot |\overrightarrow a  - 4\overrightarrow b | \leqslant 5\sqrt {21}  \Rightarrow {\overrightarrow a ^2} - 4\overrightarrow a  \cdot \overrightarrow b  \leqslant 5\sqrt {21}  \Rightarrow \overrightarrow a  \cdot \overrightarrow b  \geqslant \frac{{25 - 5\sqrt {21} }}{4}\]

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2025-3-6 02:12 GMT+8

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