⑩天掌 Teaching Plan on Advanced Mathematics nb=l‖b|c0se→cs0=4:b ,(d≠0,b≠0 d‖b 两向量夹角余弦的坐标表示式: a.tab tab cos 6= 2 2 .+a.+a 6-+b+b 2 由此可知两向量垂直的充要条件为 ib<→a.b.+a,b+a.b.=0 ZZTianjin Polytechnic University Teaching Plan on Advanced Mathematics a b | a || b | cos      = , | || | cos a b a b        = 2 2 2 2 2 2 cos x y z x y z x x y y z z a a a b b b a b a b a b + + + + + +  = 两向量夹角余弦的坐标表示式： a⊥b    axbx + ayby + azbz = 0 由此可知两向量垂直的充要条件为 ( 0, 0).     a  b 