Question

16£®ÈôÏòÁ¿$\overrightarrow{a}$£¬$\overrightarrow{b}$Âú×ã|$\overrightarrow{a}$|=1£¬|$\overrightarrow{b}$|=2£¬|$\overrightarrow{a}$-$\overrightarrow{b}$|=$\sqrt{3}$£¬Ôò|3$\overrightarrow{a}$-2$\overrightarrow{b}$|µÄÖµÊÇ$\sqrt{13}$£®

Answer 1

·ÖÎö ¶Ô|$\overrightarrow{a}$-$\overrightarrow{b}$|=$\sqrt{3}$Á½±ßƽ·½µÃ³ö$\overrightarrow{a}•\overrightarrow{b}$£¬¼ÆËã|3$\overrightarrow{a}$-2$\overrightarrow{b}$|²¼´¿ÉµÃ³ö´ð°¸£®

½â´ð ½â£º¡ß|$\overrightarrow{a}$-$\overrightarrow{b}$|=$\sqrt{3}$£¬¡à|$\overrightarrow{a}$-$\overrightarrow{b}$|²=${\overrightarrow{a}}^{2}-2\overrightarrow{a}•\overrightarrow{b}+{\overrightarrow{b}}^{2}$=3£¬
¼´1-2$\overrightarrow{a}•\overrightarrow{b}$+4=3£¬¡à$\overrightarrow{a}•\overrightarrow{b}$=1£®
¡à|3$\overrightarrow{a}$-2$\overrightarrow{b}$|²=9${\overrightarrow{a}}^{2}$-12$\overrightarrow{a}•\overrightarrow{b}+4{\overrightarrow{b}}^{2}$=9-12+16=13£®
¡à|3$\overrightarrow{a}$-2$\overrightarrow{b}$|=$\sqrt{13}$£®
¹Ê´ð°¸Îª£º$\sqrt{13}$£®

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