习题8-2
2. 已知两点与.(1)求向量的模、方向余弦和方向角;(2)求P(3,0,2)PPP(4,2,1)2121
P同向与反向的单位向量;(3)求点使得. 与向量PPPP,,2PP1212
PP,1,2,1,2解:(1),向量的模为:, PP,{,1,,2,1}PP121212
112,cos,,向量的方向余弦为:,,. cos,,cos,,,PP12222
23,,,向量的方向角:,,. ,,,PP,,,12343
121,a,{cos,,cos,,cos,},{,,,,}(2)与向量同向的单位向量:, PP12222
121,,a,,{cos,,cos,,cos,},{,,,} 与向量反向的单位向量:. PP12222
(3)设,则, P(x,y,z){x,4,y,2,z,1},,2{x,3,y,z,2}
10,x,,3x,4,,2x,6,,10252,,PP(,,)y,2,,2y即,故,所以点的坐标为. y,,,3333,,z,1,,2z,4,5,z,,3,
,,5(试求、,,使a,{,2,3,,}与平行. ,b,{,,,6,2}
,23,,,b解:由与平行得:,所以、,,,1. ,,a,,462,,