ÌâÄ¿ÄÚÈÝ
14£®Éè$\overrightarrow{a}$£¬$\overrightarrow{b}$ÊÇ·ÇÁãÏòÁ¿£¬Ôò¡°$\overrightarrow{a}$£¬$\overrightarrow{b}$¹²Ïß¡±ÊÇ¡°|$\overrightarrow{a}$|+|$\overrightarrow{b}$|=|$\overrightarrow{a}$+$\overrightarrow{b}$|¡±µÄ£¨¡¡¡¡£©| A£® | ³ä·Ö¶ø²»±ØÒªÌõ¼þ | B£® | ±ØÒª¶ø²»³ä·ÖÌõ¼þ | ||
| C£® | ³ä·Ö±ØÒªÌõ¼þ | D£® | ¼È²»³ä·ÖÒ²²»±ØÒªÌõ¼þ |
·ÖÎö ¸ù¾ÝÏòÁ¿¹²ÏߵĵȼÛÌõ¼þ£¬½áºÏ³ä·ÖÌõ¼þºÍ±ØÒªÌõ¼þµÄ¶¨Òå½øÐÐÅжϼ´¿É£®
½â´ð ½â£ºÈô$\overrightarrow{a}$£¬$\overrightarrow{b}$¹²Ïߣ¬Ôò$\overrightarrow{a}$=m$\overrightarrow{b}$£¬µ«m£¾0ʱ£¬Âú×ã¡°|$\overrightarrow{a}$|+|$\overrightarrow{b}$|=|$\overrightarrow{a}$+$\overrightarrow{b}$|¡±£¬µ±m£¼0ʱ£¬¡°|$\overrightarrow{a}$|+|$\overrightarrow{b}$|£¾|$\overrightarrow{a}$+$\overrightarrow{b}$|¡±£¬Ôò³ä·ÖÐÔ²»³ÉÁ¢£¬
·´Ö®Èô¡°|$\overrightarrow{a}$|+|$\overrightarrow{b}$|=|$\overrightarrow{a}$+$\overrightarrow{b}$|¡±£¬Æ½·½µÃ¡°|$\overrightarrow{a}$|2+|$\overrightarrow{b}$|2+2|$\overrightarrow{a}$||$\overrightarrow{b}$|=|$\overrightarrow{a}$|2+|$\overrightarrow{b}$|2+2$\overrightarrow{a}$•$\overrightarrow{b}$¡±£¬
¼´|$\overrightarrow{a}$||$\overrightarrow{b}$|=|$\overrightarrow{a}$||$\overrightarrow{b}$|cos£¼$\overrightarrow{a}$£¬$\overrightarrow{b}$£¾£¬Ôòcos£¼$\overrightarrow{a}$£¬$\overrightarrow{b}$£¾=1£¬Ôò£¼$\overrightarrow{a}$£¬$\overrightarrow{b}$£¾=0£¬¼´$\overrightarrow{a}$£¬$\overrightarrow{b}$¹²Ïߣ¬¼´±ØÒªÐÔ³ÉÁ¢£¬
Ôò¡°$\overrightarrow{a}$£¬$\overrightarrow{b}$¹²Ïß¡±ÊÇ¡°|$\overrightarrow{a}$|+|$\overrightarrow{b}$|=|$\overrightarrow{a}$+$\overrightarrow{b}$|¡±µÄ±ØÒª²»³ä·ÖÌõ¼þ£¬
¹ÊÑ¡£ºB
µãÆÀ ±¾ÌâÖ÷Òª¿¼²é³ä·ÖÌõ¼þºÍ±ØÒªÌõ¼þµÄÅжϣ¬½áºÏÏòÁ¿¹²ÏߵĵȼÛÌõ¼þÊǽâ¾ö±¾ÌâµÄ¹Ø¼ü£®
| A£® | $£¨0£¬\frac{¦Ð}{6}]$ | B£® | $[\frac{¦Ð}{3}£¬\frac{¦Ð}{2}]$ | C£® | $£¨0£¬\frac{¦Ð}{3}]$ | D£® | $[\frac{¦Ð}{3}£¬¦Ð£©$ |