Question

3£®Éè$\overrightarrow{a}$+$\overrightarrow{b}$=2$\overrightarrow{i}$£¬$\overrightarrow{a}$-$\overrightarrow{b}$=-8$\overrightarrow{i}$+16$\overrightarrow{j}$£¬ÆäÖÐ$\overrightarrow{i}$¡¢$\overrightarrow{j}$ΪÁ½¸ö»¥Ïà´¹Ö±µÄµ¥Î»ÏòÁ¿£¬Ôò$\overrightarrow{a}$•$\overrightarrow{b}$=-79£®

Answer 1

·ÖÎö Ê×ÏÈÓÉÒÑÖªÇó³ö$\overrightarrow{a}$£¬$\overrightarrow{b}$£¬È»ºó´úÈëËùÇó£¬×ª»¯ÎªÁ½¸ö»¥Ïà´¹Ö±µÄµ¥Î»ÏòÁ¿$\overrightarrow{i}$¡¢$\overrightarrow{j}$µÄÔËË㣮

½â´ð ½â£ºÓÉÒÑÖª$\overrightarrow{a}=-3\overrightarrow{i}+8\overrightarrow{j}$£¬$\overrightarrow{b}=5\overrightarrow{i}-8\overrightarrow{j}$£¬ÆäÖÐ$\overrightarrow{i}$¡¢$\overrightarrow{j}$ΪÁ½¸ö»¥Ïà´¹Ö±µÄµ¥Î»ÏòÁ¿£¬
ËùÒÔ$\overrightarrow{a}$•$\overrightarrow{b}$=£¨$-3\overrightarrow{i}+8\overrightarrow{j}$£©£¨$5\overrightarrow{i}-8\overrightarrow{j}$£©=-15${\overrightarrow{i}}^{2}$-64${\overrightarrow{j}}^{2}$+64$\overrightarrow{i}•\overrightarrow{j}$=-15-64=-79£»
¹Ê´ð°¸Îª£º-79£®

µãÆÀ ±¾Ì⿼²éÁËƽÃæÏòÁ¿µÄÊýÁ¿»ýÔËË㣻½â´ðµÄ¹Ø¼üÊÇÕýÈ·Çó³ö$\overrightarrow{a}$£¬$\overrightarrow{b}$£®